While the old town is truly stunning the best neighbourhood to stay in when holidaying in Dubrovnik is Lapad.  It's about 2 km outside the old town and the same from the new harbour of Gruz.  This is a lovely leafy area and most of the hotels are here, along with Dubrovniks two hostels.  There are also a lot of reasonable private apartments and rooms, and the area is served by several bus routes.  There are loads of restaurants and bars, and they open later than the old town.  The best beaches are located here as well so there are no shortage of options to be found.  Iva Vojnovica is the main strip where a lot of the best accomadation is and there are loads of bars here including Becketts Irish Bar.