Definitely rent a jeep to go out and explore. We recommend you head north to El Seibo and Miches (Playa Esmeralda) and then to Sabana de la Mar (Ca?o Hondo for lunch, Los Haitises tour). Just be sure to leave early so you can have a full day of exploring and be back before night fall.
On another day visit the Plantacion Tropical (Anturiana) tropical gardens in Hato Mayor. You will need a guide, but the Fun Fun Cave, also in Hato Mayor, with seven kilometers of an underground river, is also spectacular.
For Chevrolet Tracker rentals, contact the DR1 sponsor, National Car Rental at
http://www.dr1.com/national