Frankfurt-Dresden-Prague-Budapest-Vienna-Munich-Heidelberg-Frankfurt

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First of all, thank you so much for all of the great information you have posted on this website - it has been a huge help in planning our vacation!

My husband and I will be backpacking for two weeks with the above itinerary (flying in and out of Frankfurt). We have been trying to piece together different parts of our journey from other posts, but when we look at the railway websites, the prices are either unavailable or seem substantially more expensive that what we were hoping for.

We will both qualify for the youth (<26) rates where applicable.
Frankfurt
Dresden
Prague
Budapest
Vienna
Munich
Heidelberg
Frankfurt

Which is recommended for our itinerary: Ticket by ticket before we leave the US? Book departing ticket as soon as we arrive in each city?Eurail?
Any advice is greatly appreciated! We land in Frankfurt on 14Nov... nothing like last minute planning! 

I was able to find the 13euro Budapest-Vienna tickets with help from the MAV advice on the previous post.

Which is recommended for our itinerary: Ticket by ticket before we leave the US? Book departing ticket as soon as we arrive in each city? Eurail?

Though due to "last minute planning" some of the potentially cheap options won't be available, it's still doesn't mean you need to look towards Eurail pass, in terms of your itinerary it's more or less useless. So let's take a look at each leg and see what can you count on:
Frankfurt-Dresden: if your trip wasn't as soon as in a week, then you could have counted on discounted DB national tickets for direct high-speed trains. As of now there are also available for a next week, but already not for 29 euro per person (minimal fare), but more like 59, 69 and even 79 (depending on departure), so not a super option we would say. That is why it might make sense to look at special group passes offered by German Railways (Quer-durchs-Land-Ticket for weekdays or Schönes-Wochenende-Ticket for weekends), first of all it can be bought before departure (=no need to buy in advance), next it allows unlimited travel on all the German Railways network on any regional train for the whole day (=flexibility & unlimited stopovers) and the only obstacles is that regional trains are slightly slower + you'll need to change trains, though paying only 40 or 48 euro for both of you might be worth an extra 2 hours on a train compared to paying 59 euro or even 79 for one on direct train. More about DB group passes you can find on our Germany page
Dresden-Prague: here DB also offers a limited amount of discounted tickets (start from 19 euro per passenger) and on dates around Nov.20 there are still available, so if you are sure about exact date you want to travel from Dresden to Prague, then it might be a good idea to go with these 19 euro discounted tickets. You can check schedule and purchase tickets on DB website. In case you aren't sure about date or want to make additional stopover on the way, then you can do a small trick, like buy DB group pass for Saxony region (Sachsen-Ticket, 33 euro for both), use it till German-Czech border, while from there get cheap Czech domestic tickets till Prague (< 10 euro for both)
Prague-Budapest: here the best and pretty much the only cheap option is to buy in advance discounted ticket Prague-Budapest via Czech Railways eShop, tickets start from only 19 euro per person
Budapest-Vienna: as you've already figured out yourself, 13 euro discounted ticket bought in advance is good choice
Vienna-Munich: once again choices are a) buying in advance discounted international ticket for the direct train (from 29 euro per person), either via mentioned above DB website or Austrian Railways Ticket Shop (our guide on how to do it can be found here) or b) go slower by regional trains, but without need to buy tickets in advance and chance to make stopover anywhere on route. In order to do so you'll need an all Austria group pass (Einfach-Raus-Ticket, more info on our Austria page), it will get both of you to Salzburg for only 33 euro and from Salzburg to Munich you'll need group pass for Bavaria - Bavaria Lander Ticket (26 euro), both passes bought before departure
Munich-Heidelberg: basically similar options as with Frankfurt-Dresden, either bought in advance discounted tickets (from 29 euro) or group passes (Quer-durchs-Land-Ticket/Schönes-Wochenende-Ticket) purchased on the day of travel
Heidelberg-Frankfurt: since the distance between the two cities is rather short, even a full fare ticket is just a 16,4 euro per person, so it doesn't make sense to buy group pass or any kind of discounted ticket, just buy regular ticket before boarding train

Thank you so very much for your time and great advice!!!!!

With your help, we were able to take what appeared to be an impossible task and got all our tickets booked ahead of time (expect for the group passes we will get at the station).

Thank you again!!

Glad to here that you managed to book everything you need, hope your journey will be a great experience

(expect for the group passes we will get at the station).

You can book Quer-durchs-Land-Ticket/Schönes-Wochenende-Ticket/Bavaria Lander ticket online, but it doesn't really worth a hassle, since at the station (when buying via ticket machine) the fare is the same. That is why it's much more convenient to purchase it already in Germany before the actual trip

Also a small tip on how to check timetable for regional trains only (when traveling with mentioned DB group passes):

a) tick "only local transport" and b) uncheck "prefer fast connections". After you do so, DB website will show you timetable for regional trains only (thus ones you can use with group passes)

Thank you for the heads up!

We land a little before noon at the Frankfurt Airport on November 14th and want to go directly to Dresden (at the most reasonable rate)

Doing a small search as you indicated above (local only and no fast) I note that their is a savings fare avaliable for $48euro for both (Frankfurt (Main) Flugh to Dresden Hbf at 13:02)... My understanding is this is the same price as the group passes - Is this our best trainoption for the price?? (Want to have enough to when we land and it's way more reasonably priced than the fast train for around $159 euro)

Also - Can you confirm that Frankfurt (Main) Flugh is the one located right by the airport??

Thanks again for your help!!

I guess what we are asking should we go ahead and book this ahead of time (want to make sure we have a spot on the train) or should we just book Group pass the day of and take the same train/same price??

The train I mentioned above gets us into at 20:56

Lastly, we are flexible on when we leave from Frankfurt to Dresden, if there is another train station close that we could get a fast train for a reasonable price (we are seeing Frankfurt(M) Flughafen Ferrnbf  to Dresden hbf @ 14:11... We would get into Dresden 2 hours earlier albeit for $79euro vs $48 euro)

Doing a small search as you indicated above (local only and no fast) I note that their is a savings fare avaliable for $48euro for both (Frankfurt (Main) Flugh to Dresden Hbf at 13:02)... My understanding is this is the same price as the group passes - Is this our best train option for the price?? (Want to have enough to when we land and it's way more reasonably priced than the fast train for around $159 euro)

48 EUR option is exactly mentioned in previous posts Quer-durchs-Land-Ticket (you can see it yourself by clicking orange "Purchase button"). And yes, it is your best choice in terms of total fare for two passengers traveling. As was said, you can buy it right now online, but at the station it will be the same price, so purchase already on spot in Germany will give you more flexibility, since if your plane will land earlier, then you can take earlier connection, if not - later etc., while if you buy it now online, then you'll be tied to only specific connection to take.

Can you confirm that Frankfurt (Main) Flugh is the one located right by the airport?

Yes, Frankfurt(M) Flughafen is the station right in front of the airport, you can see it yourself on google maps, it's clearly visible there 

I guess what we are asking should we go ahead and book this ahead of time (want to make sure we have a spot on the train) or should we just book Group pass the day of and take the same train/same price?

Regional trains in Germany doesn't require seat reservation (it's not even always possible), so there is no need to worry about seat availability. You just board your train and take any free seat, trains are rarely full, especially when they get out of big cities outskirts/neighboring settlements

The train I mentioned above gets us into at 20:56

Just to remind you, that neither this connection, nor the one below are direct trains, but connections involving train changes. If you click on orange arrow left from the route in the schedule, it will show you all the details, station where you need to change trains etc.

we are seeing Frankfurt(M) Flughafen Ferrnbf  to Dresden hbf @ 14:11... We would get into Dresden 2 hours earlier albeit for $79euro vs $48 euro

It is option involving InterCity (IC) trains and one change in Leipzing, obviously you can consider it as well, especially if you ok paying extra 30+ euro. Though remember that since it is discounted tickets they will be tied to specific connection and train, so if somehow your plane is late or you miss the train written in the ticket, then there will be some problems. While with group pass (Quer-durchs-Land-Ticket) in similar situation you can simply take next train and don't worry about missing the previous one, group passes bought at the station aren't tied to specific train, they valid on any regional train all around Germany

Apologies for the multiple posts... We are looking for advice on another thing at the end of our trip.

Using your links above (OBB website) we found a train for $79 euro for both of us at 10:14 on the railjet... I know earlier you gave us a slightly cheaper option on slower trains (Austrian group pass to Salzburg for $33 euro and then a group pass (Bavaria) for $22 euro... our question is this: as we want to travel to Neuschwanstein Castle at some point during our stint in Germany (Nov. 21 through a full day Nov. 23rd; staying in Heildberg on 23rd night)

After reviewing your advice on the German group passes, we think it could be beneficial to combine with a trip to Fussen/Neuschwanstein Castle. What are your thoughts?

1) Vienna-Salzburg-Neuschwanstein Castle-Munich
Would the Bavarian Pass purchased in Salzburg allow us time to get to the Castle and then to Munich later on that day/night if we left Vienna early morning?

2) Vienna-(Salzburg)-Munich
Munich-Neuschwanstein Castle-Heidelberg
Or should we book the train to Munich and buy the DB group pass for Neuschwanstein Castle on our way to Heidelberg

We are flexible on staying in Munich 2 nights (Nov 21 & 22) or 2 nights in Heidelberg (22 & 23)

Apologies for the multiple posts...

No problem, that is why we are here  It's always better to ask questions first, then overpay for your tickets or "feed" the middle man selling passes like Eurail

Using your links above (OBB website) we found a train for $79 euro for both of us at 10:14 on the railjet...

Did you check same train on DB website? Though you depart from Austria, but sometimes German Railways fare for the same train might be actually cheaper. Not saying that is it will necessarily be in your case, but it's a moment on DB website to recheck

Austrian group pass to Salzburg for $33 euro and then a group pass (Bavaria) for $22 euro...

Einfach-Raus-Ticket (group pass for Austria) is 32 EUR, while with Bavaria Lander Ticket (group pass for Bavaria) there was a bit of confusion, 22 EUR is for one person, when two are traveling it's 26 EUR. Sorry

1) Vienna-Salzburg-Neuschwanstein Castle-Munich
Would the Bavarian Pass purchased in Salzburg allow us time to get to the Castle and then to Munich later on that day/night if we left Vienna early morning?
2) Vienna-(Salzburg)-Munich
Munich-Neuschwanstein Castle-Heidelberg
Or should we book the train to Munich and buy the DB group pass for Neuschwanstein Castle on our way to Heidelberg

Well, option 1 is possible, though you'll end up in Fussen early evening/evening (it's quite a long distance in total), and in November it's already dark, so not sure you'll enjoy the scenery and castle in its full. In this regard option 2 is more convenient since Fussen is just 2 hours from Munich, so you can be in Neuschwanstein Castle even before afternoon, while catching a connection from Fussen towards Heidelberg can be pushed all the way till 4-5pm (arr. to Heidelberg either at 10pm or after midnight)
As a substitution for an option 1, you can also try considering a sort of intermediate option: leg Vienna-Salzburg done by fast train (RailJet, OIC or WestBahn), buying Bavaria Lander Ticket and going Salzburg-Fussen-Munich with regional trains. This way you'll end in Fussen earlier than in option 1 (due to faster train on leg Vienna-Salzburg), though it's still be afternoon anyway. For leg Vienna-Salzburg in such case you can either buy in advance discounted Austrian domestic ticket (from 19 euro, OeBB website) or simply use WestBahn (westbahn.at) train with fixed fare (25 EUR)

p.s. also, just in order to avoid a potential problem in future, short note regarding your use of "$" sign: you probably understand the difference between currencies, but when talking about fares you keep saying something like "$48 euro" or "$79 euro" etc., it's slightly strange since $ is the sign for US dollar, while "euro" is totally different currency (roughly 1 US dollar = 0.79 EUR)