Sadly, there's no limestone in New England - just a lot of slate, marble and granite. They don't tend to dissolve and form caves like limestone does. There are a few (dry) caves in VT, but the largest is only a few hundred feet, and I'm under the impression that it's more a "pile of boulders" than a proper cave.
Here's a USGS map of the rock types in New England. According to the legend, Canada is made out of water - so that's interesting.
https://pubs.usgs.gov/of/2003/of03-225/Fig_2.jpg

