There is an Austrian with an eco-tourism hotel, focused on mountainbikers and other outdoor sports like kayak, pretty isolated, in the mountains of Ocoa. That's not too far from the capital, although getting there with public transport is a bit of a hassle.
Gira Dominicana - Rancho Cascada
Dominican Republic, Rancho Cascada - Travel, Loding & Vacation
He's a very friendly guy, and although he mostly advertises all-included mountainbike trips for bikers from Europe, I'm sure he'll accomodate someone from the capital who just wants to walk in nature.