We went to Dubrovnik a few years ago in September and for the first week visited a number of the Islands and places along the coast. Korcula, Lopud, and Hvar Town. All lovely places.
Second week was in a place called Lapad about 10 mins on the Bus (no.6!) from Dubrovnik centre, so we had the best of both worlds – quiet hotel to stay in but if you wanted somewhere to go or a night out you could go into town, which was no more than 10 mins on the bus. There was a number of restaurants near the hotel too and prices were good. We enjoyed it so much that we are going back in Sept for another little holiday. One of the nicest places i’ve been too and i’ve been fortunate enough to do a fair bit of travelling.