My husband and I were there last fall and enjoyed many of the things others have mentioned. One of our favorite things not yet mentioned was this tour:

http://www.prague-communism-tour.com/

You probably want to book in advance, the first time we tried to do it they were full.

We stayed here and really liked it: http://www.savic.eu/

I suggest visiting the Vysehrad area, which has a beautiful cemetery and a lovely church. It's up on a hill, so nice views, too. And both times we were there (October and August), it was quieter than the rest of Prague.

We also enjoyed the Alphonse Mucha museum and Communist Museum!

I love all the suggestions. I have decided to push my trip a couple of months so I can better plan my trip (and see some friends). Keep the suggestions coming - much appreciated!

one of the really fun things we did was a bike tour. I love the opportunity to "map" a city in my head and the bike tour allowed us to get our bearings. Wasn't strenuous, but fun and we learned a lot!