1. How long is the train ride from Budapest to Thessaloniki? And will there be any border along the way that needs special visa to enter? Is there an express train?
There are two good options to travel from Budapest to Thessaloniki - departing either late evening or afternoon. Both options require one change in Belgrade and take 22:30-23 hours in total
You will cross three borders Hungary-Serbia; Serbia-FYR Macedonia and Macedonia-Greece. US passport holders doesn't need visas for Serbia or Macedonia (stays up to 90 days)
2. Is it better to take a bus or train from Thessaloniki to Athens and how much does it costs?
Train ride is really picturesque, so we recommend train. Regular fare is less than 20 euro, but you might need to pay supplement or bed reservation if you choose to travel overnight or by InterCity train.
3. What is the best way to enter Istanbul and less hassle? Do I need a visa (I have US passport) and how much does it costs?
Probably to take overnight train from Thessaloniki. Quote from Ministry of Foreign affairs of Turkey: "United States of America: Ordinary and official passport holders are required to have visa to enter Turkey. They can obtain three month-multiple entry visas at the Turkish border gates." (
http://www.mfa.gov.tr/visa-information-for-foreigners.en.mfa). Cost of the visa is 20 $ or 15 Euro
4. I am also thinking of maybe taking a train from Budapest to Istanbul if that is possible? Is this a good idea?
No, as of now, direct carriages to Istanbul run only from Buchurest, Belgrade and Sofia