Not much within a day of Bimini. Gun Cay, Cat Cay a little bay called Honeymoon Bay? - been nearly twenty years since I was there. Shot my first fish
there, a slow moving but good eating trigger. The anchoring
east of Gun is not the best for holding. You have to go to the Berrys for anything interesting but I don't think you've enough time to get there and back. I would sail south from Bimini and go between Gun and Cat and have a look around.