Welcome to the forum.
Clarksville Cave, also known as Ward-Gregory Cave, is located on a preserve owned by the Northeastern Cave Conservancy. See the website here
for further information.
It's a fun beginner cave, which I've visited many times while living in the northeast. Coincidentally, I've also backpacked in Denali NP many times while living in Alaska. It's a little tough to find caves around there, though.
Enjoy your trip to Clarksville.