Why would you take the bus from Vienna to Budapest if you have a train pass? ;)
Eurail rarely makes sense the further east you go as tickets are simply too cheap. Compare with separate ticket prices first.
The pass would be useful tomorrow on Leipzig - Vienna as tickets won't be lower than 100€*. But afterwards I'm not sure...
About the itinerary I'd do something like:
- Leipzig - Vienna - Budapest - somewhere in Transylvania - Bucharest - Sofia - bus to Thessaloniki (no alternative) - Athens
For timetables you can use DB Navigator but it's always better to double check with the companies websites.
*actually 66€ by going via Prague (break there), 5:45am departure. That changes things.
I would take the bus to not have to waste a day of travel using the pass since I want to spend a few days in each city. Thank you for your response by the way! Additionally, what would you suggest I do for the rest of my travel I want to use a travel day stay in a city for a few days travel 1 day and stay a few days then once more then arrive in Athens how do you suggest I complete my adventure to reach my destination Athens? And what pass tickets/pass do I purchase to accomplish this. Thank you sincerely
p.s none of my plans or solid I just want the cheapest and most cool route to Greece.
thank you so much
Have you checked out the Seat61 guide to reaching Greece?
https://www.seat61.com/Greece.htm
It suggests the same route as @thibcabe - train Vienna - Budapest - Bucharest - Sofia. Then a Flixbus to Thessaloniki, and finally a train in Greece. It has guidance for how much you can expect to pay for train tickets if you buy them separately, where to buy the tickets, or how much the reservation costs would be if you use a railpass. But really the only way to tell is to research yourself on the relevant websites for each operator.
For example a ticket Budapest to Bucharest is around €50 in a couchette on Tuesday, according to the Romanian railways website.
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An alternative route would be to go via Switzerland to Italy, then take a ferry from one of the Adriatic ports to Greece.