For frame of refernce...I'm 25 and did VIE, BUD, and PRG (then off to Germany) 2 summers ago. Haven't been to Poland, so no comments there.
I've been asked by many, including someone from Europe wether I prefered VIE or PRG, and my answer has to be VIE. PRG is much more touristy, and is the classic favorite euro city, but I was much more fascinated by VIE. It offers probably the easternmost western city, it is fully functional while being historic at the same time. What I mean there is that everything historical and touristy in PRG is not clearly utilized by people who live there, while you see Austrians living and working all over VIE among all the history. We only did Schloss Schonbrun there (just walked, hung out, and enjoyed the city the rest of the time), and stil loved it!
I wasn't a fan of BUD, but there are some reasons for that. We did enjoy the baths, and I think you definitely have to go! Don't know much about day trips in Austria or Hungary, but in the Czech, definitely go to Czesky Krumlov. An awesome little town that is a great break from big cities. Beautiful medieval town that has survived and grown around it (again lived in...). It sees its fair traffic of schools and old people bus tours during the day, but is otherwise very quiet. The town's local brewery has probably the best beer we drank anywhere in Europe (and the cheapest!!!).
That's a good start...any ?s just ask!