East River? Not Hudson?
Likely not below Hell Gate, because the East River current can get ferocious. Yeah, there's NY Skyports Marina at E23d Street, but ActiveCaptain.com reports it's just about exclusively for megayachts, not cruisers.
Mayhaps your contact was referring to anchoring off the World's Fair Marina in Flushing Bay, in Queens, which is kind of off the East River. Several blocks south is the Flushing IRT elevated/subway rapid-transit line, which can take you to Grand Central Terminal in about 20 minutes. However, I've not seen anyone anchored there. And much of the bay is right under short final approach to LaGuardia Airport.