There are plenty of adult activities at the resort and on the island. My husband and I don't have any children and visit HH frequently. There are plenty of quiet spots throughout the resort.
There's a romantic little restaurant, the Spartina Grill, not far from the resort. It's very popular with the locals so reservations are a must during the summer months.
It's a great place for an adult get-away.
Hope you have a great trip.
Jackg57