Hull Beach (St. Thamos) really isn't secluded but there are few tourists there. The locals are very friendly. You can also get something to eat there as well as a cold drink.
http://www.hullbay.com/index.html

Jumbie Beach (St. John) is a fun place to swim and snorkel with very few people and tons of fish and turtles.

Hi There,

Hull is an excellent choice. While you are there you can try the next beach over, Dorothea. There are only a couple of condo's on Dorothea so it is almost always "under-populated". It is also very scenice, but the main drawback is that the water is too rough to go swimming.

Schultz

Hello,

Dorothea I consider a great beach to think, read, picnic, listen to the ocean... its very quiet. As Schultz mentioned the water is usually rough.

You can also rent a boat if you know how to captain it and get over to some of the litter cays around the islands. You can do this as well on St. John by renting a dinghy in Cruz Bay and beach hopping.

--Islander

On St John try:
1) Francis Bay early most mornings...snorkle out to the grassy areas and swim with the turtles.
2) Salt Pond Bay is a favorite...many don't make the drive nor the hike. Be sure to bring water with you for this one.

For something a bit different rent a boat and head over to Jost Van Dyke BVI. The beach in front of the Sand Castle Resort may not seem secluded depending on the number of sailboats that stop by, but you'll certainly get a great feeling of being a way from it all.

bob

Salt Pond Bay - I second that one. It's a lovely beach. Usually quiet like Bob said. There are no amenities there except for a portable potty. No food or drinks or anything like that. So bring a snack and water as suggested. There is a picture in the St. John guide under Beach guide. There is also a hike you can do from Salt Pond Bay - the trail begins right to the left of the beach.

--Islander