Saildiver...
The moorings that Sparky is talking about are more "dive mooring" and not for overnighting on. They are scattered all over but there are several between Cat Cay and Bimini and all around that area.
For anchoring overnight, you'll want to be in more protected waters. There is a great "storm anchor site" just south of cat cay with a sandbar to protect you from the south. We entered from the south-west corner w/o problem. Also on that secluded beach is a nice hammock you can relax in. (I think this is one of the sites you are asking about)... This is actually a smaller island that is just south of Cat Cay and disconnected by a narrow channel maybe 100 feet wide and shallow enough to wade across. There is also another great anchorage on the small island north of Cat Cay that used to be a Bahamian Defense Force station. On the north side of this island and a nice bay. I was told that this bay was called "Honeymoon Harbor". It was a great place to anchor. If you want to "tour" that small island and the old Defense fort buildings, theres the leftovers of an old dock on the southeast side of the building.
BTW... Sparky thanks to your company for putting moorings/bouys at many of these sites! It made diving much easier and also reduces risk of damage to the coral by anchors.
This website has the GPS coordinates for many of the Bouy's of Bimini
http://www.force-e.com/dive_sites/boat_diving_sites/bimini.shtml
A 23 foot boat is a pretty small boat to make the crossing from Florida in. Best of luck. You can clear Customs in Bimini or in Cat Cay, which is a private island, but the Marina is open for all. FYI that they increased customs fees a year or so ago to an up to outrageous $300 bucks per boat.
Get good charts. There are plenty of shallow spots
Check out the Complete Angler and End of the World Bar while there. (on north Bimini island). Air fills can be found at the Big Game Marina on North Bimini and at Scuba Bimini on South Bimini.
Hope that helps some. Bimini is a GREAT place.
-Mike