See
http://dr1.com/travel/puntacana/
Everything is spread out in the Punta Cana area. You will need lots of time to visit places that have been suggested.
You may also consider going west to La Romana, a two hour drive. See
http://dr1.com/travel/laromana/
You would need to rent a car and leave early to make the most of the day. Driving at night is not recommended as most of these roads are not lit at night.
Next time, fly into Puerto Plata (north coast) which is better for the free spirited adventure traveler.