25 mins drive south are these cool ruins right on the coastline. Tulum is a bohemian town that will have plenty of spots for lunch.
An adventure park with ziplines and snorkeling. Never been but have heard good things.
Much bigger Mayan ruins about 2.5 hours by car from Akumal. The town Valladolid is quite charming if you need to stop for a bite on your travels. If staying at Grand Sirenis, they will offer tours in the lobby.
For those not staying at the all-inclusive resort can buy a day pass- good from 9a-6p. Includes all your drinks and food, umbrellas with lounge chairs, pools, lazy river, and a beautiful beach with tranquil waters to swim. (Day passes are about $120)
Cenotes are these beautiful swimming holes that are speckled all throughout the area. Google search for one that appeals to you for a visit.