We were in Punta Cana a few weeks ago. Not at the same hotel but I am pretty sure it works the same way for all hotels.

If you booked threw a travel agency, you get a welcome meeting and they explain all the activities you can book during the stay. I don't know if the prices are better if you book once there. Bavaro Runner excursion offers a 20 minutes horseback riding during your day trip. If you pick Saona Island, reserve in advance, it is a popular excursion. They were not cheap 85$ each but worth it. Many water activities were also available on the beach.