Camp sites At Pigeon Lake Wildernes within hiking distance from Big Moose RR?

I started planning a different type of ADK trip. I'm in Rochester. It would be Amtrack to Utica. Adirondack Scenic RR from Utica to Big Moose Station. From Big Moose station, hike ??? to someplace to camp for a couple days. Then do the opposite and go home.

I guess after arriving at Big Moos options are North up Twitchell Rd toward Twitchell Mtn, roads East to hike in toward Contable Ponds/Cubb and Queer Lake, and maybe south to the Fulton Chain Wild Forest (not sure if there's camping there).

I'd like to think I could do 150' away from road/trail/water someplace, but ideally an official, cleared site, water would be nice is what I'm looking for. Is there anywhere close that would be nice without having to go the ~7 miles to Chubb and Queer lakes where I know there's nice sites/leanto.

Thanks.