Since you're on the upper east side, check out the World's Fair Marina.
I'm not sure if it's still called that. It's the marina on the Grand
Central Parkway, just east of LaGuardia Airport. It's 5 minutes past
the Triboro Bridge.

If you choose City Island in the Bronx, you can head uptown and cross
one of the free bridges (3rd Avenue, Willis Avenue).

You could always stay in Manhattan. The 79th Street Pier charges about
$95 per foot for year round storage. There are also marinas in Jersey
(Hoboken and Jersey City) and in Westchester (New Rochelle). I don't
know which of these may have rack storage.