Actually it's around 100 miles each way.

From Mosholu Parkway subway station below Van Cortland Park in the Bronx up Brewster is maybe 49 at the longest (about a mile less from 242nd street subway)

Maybrook study says 25 to Hopewell Junction

Apparently Duchess plus roads to go from Hopewell Junction to New Paltz is under 23

Might be an extra mile or so getting over the train yard between Brewster and Southeast

That said there look to be some north-south dirt trails west of New Platz you could perhaps incorporate. Or you can start or turn around somewhere in NYC further south than Van Cortland Park, or use the Mosholu path over towards Pelham.