As far as I know, this is the only place in the Dubrovnik old town with regular live music. Located on the Buniceva Square next to the cathedral, it's one of the best spots for nightlife in the town.
The drinks are a bit pricy in Croatian standards, though.
As far as I could see, this and the Irish bar are the two main centres of nighttime activity in the old city. The Jazz attracts a good crowd and everybody has a good time. The guys are open to stretching themselves. One night as I walked past was surprised to hear Greek Syrtaki dance music being played :-)
One thing I will say is order something easy as ther waiters are grossly overworked. I made the mistake of ordering a cocktail, which took about 45 minutes to appear and wasn't very good when it came. Stick to wine or beer!
Dress Code: None that I could see
This cool square on the eastern end of the Old Town is a great place to come and have a drink. There are a couple other bars here that give the place the feeling of being somewhat of a "nightlife central." This place is small and I imagine pretty cramped, especially during the peak season when I'm sure the crowd spills out into the square. Despite the name, there was no jazz on the night I was here.