The little town of Cavtat is a short ride from Dubrovnik.
The town itself is worth a walk (or a lunch – several very exquisite restaurants there!), otherwise you see the little islands of Mrkan and Bobara, and the coast south of Dubrovnik. Oh, and maybe, if you are in luck, you might see Eclipse, the super-yacht of Roman Abramovic, which anchors in the Cavtat Bay from time to time.