Here is a link to some excursion ideas! You can also talk to the concierge at the hotel and book excursions once you get there. We were told that you may get better prices booking excursions once you arrive.

https://www.amstardmc.com/en/excursion/punta-cana/?affiliate_id=ba73448f8e2d6c409ab4fa16a978c6fe&utm_source=amrcollection.com&utm_medium=referral&utm_campaign=tours&utm_content=en/dreams/dominican-republic/royal-beach-punta-cana/activities

There are day and nighttime activities included at both resorts. This includes things like kayaking, paddle boarding, tennis/basketball courts, beach volleyball, snorkeling, live entertainment, a night club (at Secrets). There is a spa offering various treatments at a cost and a fitness center at each resort.