Its all about the age. Maybe. Not sure. But knowing noting else, I will go with that. If you do (you probably have) some hunting on the internet you will find the lists of European In-places for younger travelers generally includes Prague, Budapest and Berlin. So you seem to have nailed that.
In sheer scope and size of the part of the city generally frequented by tourists Budapest is the largest by a factor of 7, and so the extra day there vs the others makes sense. The smallest tourist area is Prague, but its your arrival city and its got such a good reputation for your age group that the extra day makes sense to get over jet lag and for general interest.
- Thursday, Arrive Prague
- Friday, Prague
- Saturday, Prague
- Sunday, Prague
Normally I would say that compared to the other stops you are spending too much time in Prague, but you are two ladies in your mid-20’s so I think its about perfect … it holds a lot of attraction to the younger set. Personally, I am not a big fan of Prague, but this isn’t about me.
- Monday, train to Vienna. Its sort of a long trip, so start as early
as possible.
- Tuesday, Vienna
- Wednesday, Vienna
- Thursday, train to Budapest
A change from what you proposed. Vienna isn’t as much a young place as is Prague and Budapest. I just think you will find more that interests you and more to do in Prague and Budapest. Also, sounds like you are on a budget. Vienna is about the 3rd most expensive destination in Europe and Budapest is the least expensive of the places on your list. So unless its going to pay off really, really good, ehhhhh. For the Vienna buffs that are not happy with me now …. I love Vienna …. But I am not in the same category as the OP.
- Friday, Budapest
- Saturday, Budapest
- Sunday, Budapest
- Monday, morning flight to Berlin
Someone said its an 11 hour train. Probalby so. But its 90 minutes on Ryan or Wizz and prices start at about $30. Dont know why you would take a train? Okay, well, a night train "maybe" but you still lose a lot of time cause you could be out on the town at 8pm instead of heading for the train station.
- Tuesday, Berlin
- Wednesday, Berlin
- Thursday evening, I guess you are leaving ……
I didnt comment on Berlin. And wont. Not my cup of tea, but consistent with the one thing I know about the OP .... age. If you were to give up one day in Budapest, give it up for a day in Berlin. But first read what Berlin is best know for and what Budapest is best known for. Watch some videos ... okay a lot of videos. Then if Berlin screams to you louder than Budapest, spend another day in Berlin.