Like Jim said, do not bother if your focus is the beach. The Frenchman Cove beach is average at best. It is small and rocky. There are so so many better choices. It would only make the list if they allow you to use the pool complex. They can be a little protective though. I was there Friday on my check-out day, and had the beach attendant dump my stuff on the sand, since I only had a white towel (from the fitness center) on the chair.
If you want a quiet unique beach, go over to Honeymoon Beach on Water Island. It is where the beach from Benjamin Button was filmed. Take the taxi to the Crown Bay Marina, and take the Water Island Ferry ($5) over to the island. Then it is just a short walk (1/4 mile) to the beach. There is a good little food stand on the beach (Heidi's Honeymoon). Small town feel, and it was not crowded on Thursday, even though two ships were in port.
Brewers Bay right next to the airport is another nice beach. Just a beach though, no facilities or rentals. Easy to get to though - just a quick cab ride out toward the airport.
Magens Bay is a real nice beach, but can be crowded if on the weekend or more than one ship is port. Full facilities though - rental shop, bar/restaurant.
My choice would be to go to Secret Harbor. There is a great restaurant/bar (Blue Moon) right on the beach, and rental shop you can rent beach chairs for $5, and great snorkeling.
I think the current incentive for the t/s tour is $100.