There is a spot you can shore dive on the South Side. Drive straight past Stuarts Cove, past the power station a few hundred meters. You will find a gravel cleared area with what looks like a boat ramp cut out of the rock and going into the water. It is in line with the "Bond Wrecks" and Cessna dive sites on the wall. There are patches of coral in the 40ft range in every direction, but it is a long way out to the wall, about 300 meters.
This is where much of the movie "Flipper" was filmed. Stuarts dive facility was actually the movie set.
It is not a great dive site, but the best you will get.
You can also go off the beach in front of Orange Hill hotel, but also not fantastic.
Stuart might rent you tanks and weights if you are diving with him on other days.
WARNING: Nassau is not a safe island. Be very careful going to remote beaches on your own. Be wary of leaving your car unattended at this location.