
There is no limestone here and nothing was dissolved. The caves at Lost River Gorge are boulder caves: the gaps left when enormous blocks fell off the walls of Kinsman Notch at the end of the last ice age and buried the river underneath them.
The Lost River itself is a four mile stream on the eastern slopes of Mount Moosilauke, below the peak of Mount Jim, running through Kinsman Notch, one of the major passes through the White Mountains. For part of its course it disappears completely beneath the boulder field, which is where the name comes from, and reappears further down. From the notch it flows southeast to Jackman Brook, the two forming Moosilauke Brook, which runs on through the granite gorge of Agassiz Basin to join the Pemigewasset at North Woodstock.
The gorge is owned by the Society for the Protection of New Hampshire Forests, which is unusual and matters: it is a conservation organisation running a visitor attraction rather than a company, and the proceeds go back into land protection.
Getting through it is a scramble. Trails, boardwalks and ladders thread down into the boulder field and through the caves, and the passages have names earned by what they demand of you, the Lemon Squeezer being the one people talk about afterwards. Entering the caves is optional at each one, so it works for a wider range of fitness than it first appears.
New Hampshire Route 112 follows the river through the notch, so access is straightforward, and the site is seasonal.
Other places on the map within a couple of hours.