bernk - I don't use mooring balls in the BVI as I've seen too many frayed ones and rescued 2 drifting boats whose moorings had parted in light winds while the charter guests were ashore. If you are comfortable anchoring then all of the popular anchorages, with one exception, have enough space outside of the ubiquitous mooring fields to accommodate you. The exception is the Bight on Norman Island, the mooring balls don't leave much room apart from the entrance area where I and some other private boats will anchor in 50-60 feet; the charter boats don't have enough chain for that depth. And I forgot about Great Harbour on Jost van Dyke - while the water outside the mooring field isn't as deep the holding is not very good and I've had to attempt to set anchor 3-4 times before I got a good "bite" and with so many mooring balls there now it is hard to let out sufficient scope.
But if I think of Leverick Bay on Virgin Gorda the area just outside of the mooring field is 15 feet with good sand holding, even better depth and sand across the Sound at the Sand Box off Prickly Pear. The same applies to popular anchorages like Cane Garden Bay (sand, 10-20 feet), Diamond Cay (20 feet, but rocky ground), Long Bay, and Anegada.

There are also some great anchorages that are away from the crowds. I recently stayed at Long Bay for the first time and despite drawing over 8.5 feet I could still squeeze in between the reefs and anchor close to shore. And if the charter company and weather allows it, Savannah Bay is wonderful. Or the anchorage around Prickly Pear. None of those have anything ashore, so they tend to be empty.

I've not found easier cruising grounds anywhere in the world. There are anchorages there for all tastes from gregarious to hermit and everything in between.