This route connects two historic firsts -- the first lighthouse commissioned by the United States (1792, in Montauk) and the first official port of entry in the US (1789, Sag Harbor - the OG Ellis Island). It also connects the two least hoity-toity towns in the Hamptons.
If you begin in Montauk, you start at the crosswalk in front of the Montauk Lighthouse and generally follow Montauk Highway toward Amagansett (with a small detours around Lake Montauk and the back end of Napeague State Park). Rather than run through the (crazy) busy towns of Amagansett and East Hampton, stick closer to the coast along Bluff Rd and Further Ln, before cutting up across the island to Sag Harbor, through Hardscabble (how awesome is that for a town name?) and along Lost Sailor Memorial Highway. The route ends at the 'dead end' sign on Wharf street in Sag Harbor.
It's a shade over 50k and is the most enjoyable non-trail route in all of Suffolk County.