I have in laws in that area!! It is wonderful. Whether to rent a car or hire a driver depends on personal choice but may I suggest two tour services who can arrange and carry you on tours of the whole area? You can have the tours as private tours or small groups.
The first is Dubrovnik Shore Tours and they will take you to see whatever you want. www.dubrovnikshoretours.net The benefit here is that they speak the local language which is great for you if you don't speak Croatian and they know what is worth seeing.
The second specializes in boat tours. It is amazing to see the places they can take you and there are many activities they can arrange. It is called Dubrovnik Boats. www.dubrovnikboats.com
The people at both places are just fantastic.