Triarchy said:
Rum Point itself will likely be crowded, as NJGirl stated she is on a cruise ship. While the East End in general will likely be uncrowded, it is a bit of a drive and requires a rental. Id take a bus to Tiki Beach on SMB. Immediately leave the area and walk north up the beach until it gets uncrowded. It wont take long to find some uncrowded area to enjoy.
Not many day visitors get to Rum Point except for some excursions that stop in. It can be crowded on weekends because locals are there, but we've found it pretty quiet on weekdays when staying on the island. The Wreck grill also has the original mudslide, and a great fried grouper BLT.
If you don't want to rent a car just taxi to Smith's Cove, or bus/taxi north up 7 MIle Beach to Coconut Joe's Grill which is across the street from the Marriott. There is a condo property between the Marriott and the Royal Palms Beach Club. You can relax on the beach (under the tree if you're lucky) as the beach is open to the public near the water. Then stop at Coconut Joe's for a bite and drinks. Great specials and a fun spot across the street from the beach and hop a bus back
