Paradise Dive Shop
Dive. Possible with the rustic Paradise Dive Shop, or with Reef's End. They both run trips to the beautiful Glover's Reef, the infamous Blue Hole, among others.
Swim
The only exercise you could possibly hope for, short of bringing a yoga mat. while the island is almost entirely covered in sand, the water's edge is rocky, and no sandy beach exists. several piers scattered around make for easier sea access.
Snorkel
About the only activity in the immediate vicinity of the island. there's a reef along the south edge, which you can swim out to and see a decent amount of things and a bit of coral, though plastic bags and trash may keep you a little distracted. much better is to hire one of the men with a boat to take you a bit further south 1km where the sea life is much richer. day trips and 1/2 day trips that visit several snorkeling spots include mangroves to spot manatees, the reef near thatch caye, or glover's reef.
Watch 'em gut a fish
Around sunset, on the western pier in front of tobacco caye bar, local fisherman prepare their fish or ones caught by fishing tourists and wash them here at the dock, drawing a little crowd of onlookers. fish guts may not be that interesting, but the animals that swarm in to eat them are... you'll likely spot a variety of birds, stingrays and even a moray eel all converging on the scene.
Bring a book
If none of the above appeal to you, or you've already done them once today, find out what happens after sally catches bob with sue.