Coral Bay is fun with Skinny Legs and Indigo Grill at the Dinghy Dock, we prefer to anchor at Hansen Bay (in Coral Bay) for great swimming and snorkeling.
Little Lameshure, Great Lameshur and Salt Pond are great south side anchorages with NPS moorings. BabandRon mentioned hiking from Lameshur to Reef Bay, but there are also day use moorings at Reef Bay. There is an NPS dock at Lameshur with trash drop off. You cannot see any houses/lights on the hills above Lameshure. From Salt Pond it is possible to hike up to Concordia or the Tourist Trap for food and drinks. Concordia has a small camp store.
We love Leinster/Waterlemon Bay with great snorkeling and access to the Johnny Horn Trail and Annaberg. Walking up the ridge you get a great view down the Drake channel. You can hike to Brown Bay or go all the way to Coral Bay. This is one spot with almost no ATT/LIME/Digicel access. The outermost mooring has a bit of ATT signal.
The Maho/Francis Bay anchorage is our favorite. Lots of moorings that are spread out and generally well protected. The Francis Bay side has a better breeze coming over the low lying area.
You can access Trunk Bay and Cinnamon Bay from the moorings there. Not so well protected. Hawksnest also has moorings.
The Caneel Bay mooring is exposed to ferry wakes that run from about 5AM until midnight. The closer in towards the Caneel dock the less rolly. You can dinghy up to the Caneel dock to access the restaurants. Zozo's is a crowd pleaser. The Bar & Grill has well reviewed sushi at lunch. They usually ask you to put out a stern anchor for your dinghy.
We prefer to have our play time in Cruz Bay and anchor elsewhere since our monohull feels like a rocking horse in the Caneel Bay anchorage. But, Cruz Bay has so many walkable shops, bars and restaurants we end spending the night there more often than not. As others mentioned, Christmas Cove at Little St. James is a great close anchorage with Pizza Pi.
Not too far down the south side of St. Thomas is Abi Beach Bar. Its a polished interpretation of the beach bar style. We like it.
If you're checking in at Cruz Bay you can anchor in the creek area close the C&I if you draw 5' or less. Don't try and approach the C&I dock with a sailboat. The NPS dinghy dock is a short walk to C&I. Make sure you dispose of trash before you check in at Cruz Bay, otherwise they will ask you to take your trash to an incinerator on St. Thomas.
Here's a useful NPS mooring guide:
http://www.nps.gov/viis/planyourvisit/upload/MooringGuide.pdfCheers, RickG