Welcome!
Try connecting with local cavers sometime, and maybe you can get on a trip. Information on the Southern New Hampshire Grotto, and the neighboring Boston Grotto, can be found here.
http://www.caves.org/io/iolookup.php?state=NH
There are also grottos (local chapters of the National Speleological Society) located in Vermont, Connecticut, and upstate New York - to name a few. Most of the folks don't bite, and you'll likely be welcome to join them on a beginner-level trip if you don't mind a little driving to get there. You may even get to visit some bats.
Good luck!