We do have a tour that goes to the sugarcane fields where you will visit a local school, fruit and sugar plantations, as well as having lunch at a typical ranch. It is very much off the beaten track. You can see more info here:
Tours
If you want to go more solo, renting a car would be your best option. Chiri had some good suggestions or you could take a drive to Hato Mayor (very Dominican town with the popular Cueva Fun-Fun, Playa Juanillo in south Punta Cana (one of the top beaches on the east coast and very tranquil), or take a longer drive to Miches and the amazing Playa Esmeralda.