Check out the Welcome Punta Cana guide authored by the editorial director of dr1.com
See link at
Punta Cana - Dominican Republic
The guide lists many of the excursions offered by tour operators to tourists staying in the area. Of course, many of these can be done by tourists themselves, without booking the excursion. More time would be needed to be allotted, and in most cases, it would be best to rent a car.