These are three great cities, as all the above posts indicate. Here are a couple more things you might not want to miss.

In Prague, visit one of the beer halls. U Fleku (I think the name's right) is one of the great ones. And if you get a chance, drink Budweiser... the REAL Budweiser, for which our pale variety is named.

Buadapest: Have dinner one evening at the outdoor terrace of the Gellert Hotel, overlooking the Danube. A bottle of wine, a great meal and the small orchestra playing a charadash will leave an enduring impression.

Budapest: Don't miss the LaHar theatre, not far from the Marriott. Great pop-operetta, wonderful Hungarian music... a rollicking, lively evening with mostly European tourists.

The baths are such an important part of Budapest life that you should experience them. Try the baths at the Gellert Hotel, even if you're not staying there. You'll see old men playing chess in the water, young women... well,it's a great experience.