We stayed at the Divine III for three nights in early May and we were really sad to leave. Divine III is a great little apartment in the very heart of Dubrovnik's Old Town - and is a perfect location for visiting the main tourist sights.
The apartment is in a side street off the Stradun, and is surrounded by decent restaurants (you have a choice of two pizzerias as you step out of the door - though be warned, the pizzas in both are massive). There's a small but fair Konzum supermarket about three minute's walk away (at Gunduliceva Poljana, with a fresh food market in the same square on most days), an off-licence and a host of other restaurants within a stone's throw. Initially we were concerned we might be too central, but had no problems with noise at all.
The apartment itself is immaculate - newly and nicely decorated, with a fully functioning oven, hob, dishwasher, and washing machine. All the crockery and cutlery you need is provided, with a selection of condiments and cleaning liquids inherited from previous tenants (FYI - you'll need to bring your own bathroom toiletries, though towels are provided).
The apartment has a video on Youtube, so you can decide if it is the place for you (search for Divine III, Dubrovnik)