Don't waste your time. Bimini is just a place to refuel and check in. If you have more time, go to the Exhuma chain from Bimini (midway stops at Berry Islands and Andros). Will cost you $100 just to visit Bimini. The other problem is that you can get stuck there due to weather needed for crossing the gulf stream, although April isn't too bad. The Keys are a good alternative if you have time restraints. You can stay inside, along ICW, or do the Hawk Channel. Islamorada is pleasant, but my favorite spot is Marathon, with its well protected harbor and great boating community. You can pick up a mooring, anchor just outside, or use a marina. We've stayed there for weeks at a time. Key West is expensive to take a boat, and has no good anchorage. We usually stayed in Marathon & rented a car for the day to do the 60 miles to Key West from there.
Dante