Talus caves in the boulder jumble near Millinocket, deep enough and shaded enough that ice survives in them through the summer, sometimes into August. You climb down a ladder into the main one and the temperature drops thirty degrees in a few feet. The trail in runs through the Debsconeag Lakes Wilderness with Katahdin in the distance. Bring a headlamp and traction, because the floor is literally ice in July. The trail runs about a mile from the parking area over uneven rock, starting behind the gate at the far end, and rebar ladders drop you into the cave itself. Open to the public with no fee and no permit; camping only at designated sites, and fires by permit only. PUBLIC trail (Nature Conservancy, 46,271-acre Debsconeag Lakes Wilderness Area), near Millinocket.
Other places on the map within a couple of hours.