I second many of the suggestions on the thread, especially:
Las Galeras and Playa Rincon
The South West
Moncion Dam, Santiago Rodriguez
Mao and Punta Rucia/La Ensenada
Constanza
The East - El Seybo, Miches
No one mentioned Isla Saona, though. You can take boat trips to the island from Bayahibe or Boca de Yuma. Isla Saona is a controlled reserve. Only local people are allowed to live there. Great scenery and good snorkelling/scuba diving in the area. You can have lunch there but you can't stay overnight.
Another scenic area near the capital but largely unknown is Yamasa/Bayaguana - unspoiled 'real' rural DR with plenty of natural treasures like waterfalls and rivers.
Las Galeras and Playa Rincon
The South West
Moncion Dam, Santiago Rodriguez
Mao and Punta Rucia/La Ensenada
Constanza
The East - El Seybo, Miches
No one mentioned Isla Saona, though. You can take boat trips to the island from Bayahibe or Boca de Yuma. Isla Saona is a controlled reserve. Only local people are allowed to live there. Great scenery and good snorkelling/scuba diving in the area. You can have lunch there but you can't stay overnight.
Another scenic area near the capital but largely unknown is Yamasa/Bayaguana - unspoiled 'real' rural DR with plenty of natural treasures like waterfalls and rivers.