Hi psinyc,
Stuart Cove's
http://www.stuartcove.com/ is on New Providence, sometimes referred to by its capital, Nassau. It, along with Nassau Scuba Centre & Dive, Dive, Dive, Ltd are located in the far SW of the island. All dive the same spots. Except for Dive, Dive, Dive, Ltd, with whom I've had some unsatisfying experiences, I recommend them. IMHO, the dive sites in the main are just so-so.
Yes, Coz is almost exclusively drift diving. All Coz ops dive most of the same sites, including Devil's Throat if the group has the needed skills. The Devil's Throat, or La Garganta Del Diablo in Spanish, is a site in the Punta Sur area, with Columbia Reef to the north & Chun Chacaab to the south. It's not a cave, but rather an extended swim-through. It exhibits a relatively gradual slope through most of its extension & in many places has room for two divers either side-by-side or over-and-under. Although dark in spots & an overhead environment throughout, at all or nearly all points during the dive you will be able to see some a route of escape with ambient light, although at times this will be behind you. The entrance is at about 75'-80', and it exits at one of two main openings, one to the upper left at about 116', and another to the lower right at about 127'. It is quite a sight to exit and look out into the blue, but it is not abyssal--about 55'-65' from where you exit you can see an expanse of sand & patch reef bottom tapering downward.
Got carried away there, didn't I? Anyway, I stick by the recommendations & conditionalizations in my original post.
Have fun wherever you go.
DocVikingo