Roads in and around Dubrovnik are decent, even if some renovations would be desirable. The traffic in Dubrovnik will probably be quite heavy, you could experience parking problems depending if you will visit Old Town often by car. I suggest you try public transportation (busses) or walking as a better way of getting around Dubrovnik.
As for the places to visit I recommend Peljesac peninsula, Island Korcula and Mljet (ferry departures from Orebic or Dubrovnik, Cavtat, Molunat…
Generally, there are numerous small towns and villages along Dubrovnik Region, take your time to explore and drive carefully.
I think the best option is to go with an agency; you can also make online inquiries and reservations through our guide.