I'd go to East Beach or the Charlestown Breachway. Last weekend the birds were working the entire length of the beach. They were to far out on Sunday but Saturday they hit them hard.
Be sure to move around; almost all the spots in the SoCo area had fish but they were all twinkies. We left fish several times and eventually found decent fish between 15 and 25 pounds feeding on mackeral and bunker.
Either that or your idea to head West to Montauk sounds real good too.