I just returned from a week in the Bahamas. There are two dive operations on New Providence, I think the others have gone out of businesss. I dove two days with each operator and I think either is a fine choice. I hope to post reviews of each operation, as I had a hard time getting good info myself prior to the trip. Here's a few comments on each one.
Bahama Divers
Good location just across the bridge from Paradise Island. If you are staying on Paradise Island this is a nice advantage, short bus ride from the hotel. You can reserve your dive days with them directly or through your hotel. Small, very efficient operation. One boat which is a bit old but works just fine. Crew and divemasters are great. At least one of them will be in the water with you, along with a video guy. They really push the video, but it is a nice video. Boat left precisely on time each day. Upon return they give you plenty of time (too much for me) to preview the video and browse the shop before the bus leaves back to the hotel. I was rushed for time my last day with them and actually caught a cab back.
Dive Sites: Bahama Divers dives the NE end of the island. It seems that the dive sites on this end generally aren't quite as good, but are still decent. If the predominant NE winds are blowing it can be a bit rough. They advertise the Lost Ocean Blue Hole trips for Mon, Wed, and Sat. I went out with them Monday but they changed it to Trinity Caves due to weather. Other divers on the boat said they've dived several times with Bahama Divers and have never made it out there. It's further from shore and takes more time. I sensed a possible bait and switch. When I dove with them Saturday, the seas weren't as high and I almost insisted that we go there or I wasn't diving with them. Amazingly, we made it out there and it was an incredible dive. The nearby Barracuda reef was very good as well.
Stuart Coves South Ocean
I had read some bad things about this place so went there a bit biased. It turned out to be OK. It is a long bus ride to the SW side of the island, longest from Paradise Island. But being on this side protects them more from NE winds. If they are busy, you'll have a long wait at check in. The first day with them was a busy day and I ended up on a combined snorkel/dive trip. Avoid this situation if you can. The first dive was too deep for the snorkelers but they made up for it by chumming for sharks. This was cool as we had plenty of finned company on our dive. Dive 2 that day was just offshore and good for snorkelers but poor for divers. On my second day for them, one lady insisted we go to Playground after she had a bad experience (the boat had a scuba class the prior day). This turned out to an awesome wall dive, the captain agreed to go out there and SW Reef was Dive 2 and also good. I think the further from shore you go the better it gets (as far as condition of the reef). We only had seven divers that day, all experienced, and it was great. I think the Stuart Cove experience varies based on who's diving on a particular day. Avoid afternoons as they seem to get more cruise ship snorkelers and beginners. More serious divers seem to do the morning dives. SC does have awesome t-shirts, I picked up three of them.
Hope this helps. I was comfortable with both operations, it was good to get wet. I'd even suggest trying both (as I did) to go to different locations. Definitely try for the Blue Hole with Bahama Divers if you can get them to go out there.