Even if you decide that diving underground isn't for you, cavern training is a great way to improve OW skills. On my first OW dive post-cavern I was amazed at how much my buoyancy and trim had improved and how overall more comfortable I was in the water. The course was more than worth it for that alone. As mentioned previously, there are a number of privately owned sink/caverns in the area that allow AOW divers (although some only without lights), but the cavern course gives so many additional skills that it's very worth the time and money.
On the last day of my cavern course my instructor took me into the cave, through the gallery and into the lips at Ginnie, where I hit 1/6ths on my AL80. I was thunderstruck -- could not believe there was a place like that on Earth and that I was in it. Got my Cave I, and am now diving cave every chance I get, working up to my next (full) cave course next year. Still dive the salt sometimes (I'm not a purist), but more in the fresh. Of course if you do get bit by the bug, you know all that money you spent on gear and training so far? A drop in the bucket once you start gearing up for cave. Of course, once that's paid for, a cave is cheaper than a boat trip.