Definitely possible. I have been to Sarajevo and the Dalmatian Coast. I recommend both, especially trips out to the Islands in Croatia or down to Dubrovnik.
Budapest is marvelous. Make sure you go to the baths (I went to the Szechenyi), but it's probably a mistake to go on one of the men-only days. Unless you're into that.
I was there in November 2004... did the Prague, Vienna, Bratislava, Budapest, Krakow route (then back to Prague). Budapest was the best of all those.... followed by Krakow.
I also was in Budapest in 1994. It is a great place. I particularly remember a great meal at a place called the Gundel House. Also, there is a park outside of town with all of the communist era statues. That was way cool.
There is a novel called Prague by Arthur Philips that is actually about a group of American's in Budapest in 1990. It is a good book and captures the city and that era well.