united states virgin islands
The US Virgin Islands are well-known and definitely well-visited. Space is limited, so prices are high. Fortunately, St. John is a national park and is somewhat protected from overdevelopment (although it's still pretty developed).
We spent a week here, staying in a more affordable place way up on a hill. We rented a tiny car and would drive to different beaches everyday, and did a few gorgeous hikes around the island. The highlight for me may have been finding old sugarcane ruins left in the jungle from the times of pirates.