I'm Searching on the internet....and here I guess.
Unfortunately you‘ll need to make a lot of calls. If you don’t know the areas you can find the listings in navigation apps like Garmin Boating (Navionics) or Aqua Maps which let you load the ActiveCaptain and Waterway Guides info. You could also search Google Maps for Marinas by area.
Considering the traffic and drive time already discussed I am wondering what your plan is with a 20 foot boat. It wouldn’t be practical unless you plan to stay for at least a couple of nights. If you’re thinking about using your O’day Mariner you’ll be “camping”, and a bigger boat with more comfortable accommodation would be better.
You may also consider trailering the Mariner and staying in a hotel or Inn when you’re not out on the boat. There are many free or cheap public launch ramps all along the coast in great areas.
Western LI Sound is often in doldrums in late July/August, and the water quality is awful for anything more than wading. The better sailing is in eastern CT and RI, and you should also consider the eastern Long Island forks area (Greenport, NY) where the daysailing is great in Gardiners Bay and the water is beautiful.
Edit: Many yacht clubs have cheaper moorings, and some even have ramps. Even with the membership dues added, it might make economic sense and come with added social benefits.