Hi Rob,
The Elaphites are very nice and highly recommended by lots of people.
However, if you really want to chill out and relax and leave the world of work and stress behind for a few days I couldn't possibly recommend anywhere better than the Island of Mljet. I wrote an article for a paper (for no payment) some time back because of my love for this place (http://www.irishtimes.com/newspaper/travel/2008/0712/1215769290111.html).
As far as my memory serves me, a ferry/catamaran called the Nona Anna leaves the Dubrovnik Ferry Port each morning at about 9am for Polace on Mjlet. Polace is only a tiny little half moon bay with some restaurants and rooms to rent. For Croatia, it even has the luxury of a beach, albeit a shingle beach.
When you get off the ferry just ask the first place you find for a room, there's some nice appartments over the shops and restaurants along the sea front. The food in the restaurants is fantastic and so fresh you can see the owners taking their boats out in the morning to lift their lobster pots etc...
It's a small place but there's plenty of fantastic walks, a lake with a monastery in the its centre, it's a National Park with dolphins and crystal clear waters. Also the island is famous for its wild mongooses, they were introduced to take care of a snake problem they once had.... no more snakes I hasten to add.
Anyway that's my recommendation. It may not be everyone's cup of tea but if you decide to go and like it maybe you'll send me a PM to let me know.
I realise that my post probably sounds like a promo piece but the truth is, I've no other interest in the place except I fell in love with it and I'd like other travellers to do the same (but not too many, ok!)
Fell free to PM me with any specifics.
Zaksame