Help! Trying to price ticket to ticket In Europe

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I will be traveling in May this year and need help pricing tickets.  Am going from Rome to Budapest; Budapest to Prague; Prague to Vienna; & Vienna to Paris.  Is a pass cheaper?
Had trouble navigating Trentatalia & Czech train sites.
Thanks

Am going from Rome to Budapest; Budapest to Prague; Prague to Vienna; & Vienna to Paris.  Is a pass cheaper?

We aren't sure about exact pass price for you, thus lets count:
Rome-Budapest: since there is no direct train here, low-cost airlines flights here will almost always beat train fare (for instance WizzAir). If you specifically want to use trains, than you will have to catch Italian domestic train Rome to Venice (discounted fares start from 29 EUR in case of EuroStar or even cheaper in case of IC or ICN trains). Venice-Budapest route is served by direct overnight train (NB: train goes via Croatia, so be prepared for full scale border/customs controls), there are also discounted tickets available, seat from 29 EUR. But in both cases discounted tickets need to be purchased in advance from TrenItalian website.
Budapest-Prague: here also discounted international tickets is available (from 19 EUR), but unfortunately Hungarian Railways website interface for online sale currently only in Hungarian language, so you will either need to use google translator or purchase tickets already in Budapest (but need to do so at least 3 days in advance).
Prague-Vienna: same story with discounted ticket, start from 19 EUR and Czech Railways offer easy English interface for online purchase - https://www.cd.cz/eshop/international/search_int.aspx?tt=3
Vienna-Paris: no direct train or discounted fares available, so your best choice here either to fly directly (AirBerlin, FlyNiki etc.), fly from Bratislava (hour by train from Vienna) by RyanAir (tickets usually much cheaper than in previous option) or get discounted ticket Vienna-Munich (from 29 EUR if purchased in advance - https://ticket.oebb.at/bin/frame_ticket.pl?ticket=jticket.pl&LANG=EN), from Munich you can actually catch direct train, discounted tickets are also available (from 43 EUR - http://reiseauskunft.bahn.de/bin/query.exe/en?newrequest=yes&protocol=http:&).

We also might recommend changing you sequence of cities to Rome-Budapest-Vienna-Prague-Paris, this will save you travel time (no need to come back southeast from Prague) and money (from Prague there are cheaper direct flights to Paris (comparing to route Vienna-Paris) - Smart Wings, EasyJet etc.)

Thanks for the info. I know it looks like we're going the long way around to go to Budapest from Rome, and that's because we are!
But, we're meeting friends in Prague and going to Vienna with them & I just wanted to see Budapest on this trip.
I didn't think about looking at planes after our itinerary was set Good idea!