We did a jazz cruise on the river one night, which was really nice (went for my 40th last year!). The food was surprisingly good and the vibe was laid back. We liked the Jewish Museum too. The castle was a bit boring IMO, but the Cathedral of St Vitus was good and I really liked the stained glass window by local artist Alphonse Mucha. There is a museum of Mucha's work too, which I thought was lovely (google his posters - they're art nouveau and you're bound to recognise them as they're very famous).
Have you read HHhH? If so, be sure to visit the crypt of the church of St Cyril and Methodius as its there Heydrich's assassins made their last stand. Its very moving.
Do a 'free' walking tour. They're not really free, but you are expected to pay your guide what you think the walk was worth. We had a very knowledgable guide and saw places that we would have missed. We also went (because of this walking tour) on a train to a concentration camp called Terazin which was very moving with another walking tour guide. Prague is beautiful. We went in December 2013 & saw the Christmas market.