We had a 4-day break there recently, staying at the Questenberk Hotel. It hasn't got a bar but there are several cafe-bars within a very short distance, incuding the one within the monastery, where the monks brew their own beer!
In fact, the hotel was part of the monastery - which is, of course, one of the "sights" - originally. Excellent accommodation and staff, great views down to the city, away from the throngs of tourists, close to the castle and a tram-line, so easy to get to places. Not cheap, but thoroughly recommended.
If you go, have dinner at the Little Blue Duck, just round the corner from the Lennon Wall. Good luck!