Cane Garden Bay is a nice crescent beach with several bars and restaurants on it. Also mooring balls so you can spend the night if you want to. Just don't go on a cruise ship day or during a north swell.
Sandy Cay is more the deserted island beach where you typically only get boaters since you need a boat to get to it. Green Cay is close by as well and is smaller but similar.
The north side of Anegada has some great beaches - Cow Wreck and Loblolly in particular. You don't dinghy there but rather take a taxi or rent a car from the anchorage which is on the south side of the island.
Those are the best three that I can think of where you can generally stay at the whole day. If you get to the USVI there are also several good beaches on the north side of St. John.
