Lots of opinions, no right or wrong answers. If leaving Narragannset for NYC, I personally would skip Block. It's a little out of the way anyway and not my favorite place, but like I said, some people love it there. You'll also bypass the Race, which can get hairy at times. I've never been to Stonington by boat but it's a pretty harbor. I hear the yacht club is great and they welcome transients. I happen to love Noank and the Noank Shipyard marina which is the first you will see entering Mystic river from F.I. Sound. Great seafood at the marina and next door at Abbotts. There are so many great stops in that part of CT, hard to go wrong. Essex is worth the trip if you've never been. Griswold Inn is a unique and amazing place to eat/drink. Unlike Prh above, I'd advise against the Thimbles as much as I love it there. Navigating can be tricky with lots of underwater rocks, and anchoring can be hit or miss depending on the wind and waves that day. Better left to locals or someone who has been there before. Clinton has a great marina but no anchoring really. Branford is also great for either. Once west of Branford you are better off on the south side of the sound. Mattituck is the first possibility, then Port Jeff. PJ is almost a must, especially for the large mooring field and anchorage just west of the harbor entrance. Follow the shore. The town of PJ is OK, little touristy, but good if you want restaurants. You can get a mooring from the yacht club with launch service. There is also a pumpout boat that will service you at anchor or a mooring. From there you can reach NY or any of the other harbors on Long Island as you head west. Time Hell's Gate so you arrive there at high tide and you will ride the current into and out of it with no standing waves or strong currents to deal with. Never anchored behind the statue, but lots of boat traffic in the area so not sure how calm/rough it may be. Liberty Landing is expensive but very nice facilities and restaurant. The plus is you can catch a ferry from there into lower Manhattan if that interests you. Some great places to eat/drink if you know where to go. Going up the Hudson, try to time the tides if you can. I like Croton Point as an anchorage. Protected and good holding. I prefer the north side inside the "elbow" but depends on wind direction.
Lots to think about. You could spend the whole summer in Long Island Sound so hard to pick 1 or 2 favorites. If you begin to narrow down your itinerary I'm happy to provide more details on any particular place. Could even meet you along the way. For instance PJ is only about an hour ride due south across the sound for me. Hope that helps you get started. Enjoy the trip!