The closest listing to Montauk is Hither Hills State Park, about 4 mi away. 15 places to camp sit within 50 miles, 41 within 100, and 86 within 150. Every one carries weather, wildfire proximity and a straight link to the official booking site, and the federal ones show live availability.
Federal campgrounds where the app shows how many sites are open tonight.
A lake, river or beach you can get into from camp.
The listing says pets are welcome. Leash rules are on each one.
An agency document names accessible sites. The source is on each listing.
15 more in this range on Campgrounder →
Distances are straight-line miles from Montauk, not drive times. Mountain roads can double them.