reasonably close to NYC is Mamaroneck, NY. you can try Orienta Yacht Club [45 min on MNR direct to Grand Central, and only 12 min walk from the club to the station], they [or should i say "we", as i'm a member
there] have 2 guest moorings. moorings are double moorings (stern+bow), the harbor is a hurricane
hole, and although we're past summer hours there's still decent launch coverage. i forget what the daily rate was, but there are showers at the club house (not much more). it's also right next to McMichael's who can help you with repairs
should you need anything (and they are really great guys, although not cheap).
if you want to be closer to the city, there's the newportmarina right off the Newport/Pavonia PATH station. they have docks, you'd need to call and find out the rates and availability. but given that off-peak r/t MNR ticket from Grand Central to Mamaroneck is $17 now, depending on how many people you have and how many times you'll want to go to the city, paying more in docking
and less in public transportation costs may be cheaper.
the 79th st basin is so far up the Hudson! you gotta time it going up, and you gotta time it going down, and it's very choppy with all the water taxi traffic (the same applies to anything on the Hudson, btw, so the one night i slept on the boat in Newport/Pavonia wasn't much fun, but it was a small boat and i was on the outer docks, so you should ask them where exactly they would put you) makes it feel like you're always going down Buzzards Bay in the wind
against the current
chop, every 5 minutes.