Before I go anywhere I consult my 1000 Places to See Before You Die book. It is a great resource for off-the-beaten-path ideas. For St Thomas the recommendations included Magens Bay Beach. I will give them that it is unspoiled. Not a big resort in sight.
I much preferred Sapphire Beach on the other side of the island. I think the name sums it up nicely. Sapphire water, nice sand, great waves. This was an all around great beach. You can even make friends with the sunbathing iguanas.
As long as you are there take the short hop over to St John Island, it is only a ferrie ride away. Keep your eyes open for great photo opportunities along the way.
On St John I quickly abandoned the tourist shops at landing and took the local bus to the trailhead at Cinnamon Bay. Riding the local bus up provides you the easy hiking down to the beach. This is a nice walk with the opportunity to see some amazing mud nests. Keep your eyes open for glimpses of the beach as you pass openings in the flora. At the end of the trail there are some ruins of a sugar plantation. Be sure to check them out.
Your ultimate reward for the hike is Cinnamon Bay beach. It is a wonderful place to spend a afternoon after your hike. There is camping available at the beach also. When you are ready to head back to St. Thomas there is a very convenient shuttle to the landing to catch the boat.
All in all the USVI is a great place to catch a little sun, decompress and relax.