Ooh yeah! Good times out there are to be had, for sure. I've flown quite a bit to the Bahamas and although I've been there many times, I still have a lot to explore about that place. First of all, unless you just have to gamble or must see Atlantis (which is hands-down the most amazing resort I've ever seen), avoid Nassau. You will pay top dollar for going through customs, landing fees, and parking fees. If you do head out there, enter customs through Avitat on the East side of the field. They don't charge much for parking (compaired to Signature or Million Air on the South side) and their facilities are top-of-the-line.
If you just want to island hop, Bimini is a great port-of-entry so that you can head anywhere from there without having to concern yourself with customs (although if they are on the field, you should check in with them and show them your itinerary). North Bimini is a short taxi and boat ride away from the airport, and has some wonderful hotels and restaraunts. Watch out for the noseeums... they suck.
Avoid Freeport. Trust me.
Andros island is beautiful as soon as you get away from the airport (which is tough).
Treasure Cay is an old-people's resort island. Lots of private property there. A bit of a bore. Also a long drive from the airport to anything relatively exciting.
I give five stars (as long as you're looking for an adventure) to Norman's Cay. It has a tiny bar, some bungalos, and an airstrip... and the most beautiful beach. Just watch that tide.
Finally, don't expect to be allowed to fly at night unless you're IFR rated and in an IFR aircraft. Not only is it required, but you'll need it.
Hope this helped. Good luck, and have fun with the rest of the Caribbean.
PS: Don't look like a rookie... Cay is pronounced "key".