We stayed at The Caves twice, most recently 1/11. Both times we passed on the cave dinner, we checked it out and it was just too damp and humid for us, it was much more pleasant sitting outside with a nice breeze in the normal dining spots. They do have a nice private table for two in it's own little alcove looking out to the sea, but I don't think non-guests can book that.
If you're interested, email the hotel or call the toll free number, I'm sure they can give you the details, but I think it was $300 or more, probably not including wine.
If you want to check out the place, The Sands bar is open to the public on Wed and Sat afternoons I believe. They have some jerk you can purchase and there were local cliff divers there. Much better than going to Rick's. There's a 30' jump there that's real safe, many guests and visitors were doing it. Not me, I'm a chicken.