Budapest/Prague
A friend and I will be visiting Prague next month as well. Although we have not set up our itineraries yet, we know that we'll be staying at Hotel Josef (a new contemporary hotel in the Old Jewish district). I was in Prague 12 years ago and frankly don't remember much of what I saw except for the Charles Bridge.
I went to Budapest in 1999 and three things that I remembered most are Gellert Bath (the most beautiful thermal bath I have ever seen), Kiraly Bath and the Opera House.