I can help you with some of the cities
Vienna - Stay at Wombats hostel. Reasonably priced and safe, even if it is by a lot of places that look like they could be "chop shops". It is also five minutes walking from the main train station and a couple minutes from a metro stop. The city is a little expensive though and it is a must see for people into art and classical music/opera. Otherwise, it can be a little bland.
Berlin - Circus Hostel was the best hostel I stayed at in Europe. For something cheaper, Arena Hostel is very cheap and located across the street from the Zoo Station. So much to see and do in this city, it is really an amazing place, but East Berlin has more to offer to the backpacker crowd (more culture, cheaper prices)
Munich - I was at Euro Youth Hostel. It is about five minutes walking from the train station so it is centrally located. Only about ten minutes walking from Hoftbrahaus, but it will feel much longer after a few beers there. Euro Youth Hostel is also owned by the excellent, and less touristy Augistiner Brewery. Englishcher Gardens (sp?) is a great place to just spend a day walking/biking through
Budapest - I stayed at Marco Polo Hostel. While it is nice, it is very expensive for a hostel (25 euro for dorm room). There are others that would be better value probably. The city is somewhat like Prague. It is also quite expensive for a Eastern Europe town.
Prague - I have stayed at several hostels here. I would suggest The Boathouse for an excellent hostel, but it is a 15 minute tram ride from outside the city center. For a central hostel, Apple Hostel is right in the center and about 9 euro a night, but it was not the best hostel experience (but not the worst).
For flying,
www.GermanWings.com has cheap flights out of Cologne and Stuttgart to many places including some of the cities you want to go to so check them out. Since you are out in the region, Poland is worth checking out especially Krakow. Other cities to check out in Czech Republic would be Olomouc and Cesky Krumlov.