We usually time the current up to Liberty Landing Marina. Not cheap, but they are really crowded at all during these Covid days. Behind the statue the anchorage is nice and not to rocky. Definitely time the currents of the East River. It's a beautiful and exciting trip. If you time it right you can add an additional 5-7 knots to your speed and push you right up to City Island. A nice place to stay is City Island, by the way, quieter on the weekdays and a bit of a party town on the weekends. The Black Whale is an excellent place to eat. Oyster Bay is beautiful place to anchor and also Oyster Bay Marine is a nice marina, with a popular bar/restaurant. Dockwa says they only do mooring balls, but call the Dock Master and you can get a transient slip. I would jump over to the CT side if you can. Norwalk, Milford, Mystic are all beautiful places. Definitely stop at Greenport, just around the northern fork of Long Island. They have an amazing merry-go-round, great restaurants, excellent clam bars, and a cool hot sauce shop. If you have time swing over to Block Island, and check out the Hamptons. Greenport will set you up to travel through the bays and the lock heading south. The last time I went through the lock it was open and we were able to just transit through it, but you have to time it right to do this. Southern LI really doesn't have a lot of great marinas available the last time we did this, so anchoring is a great option, as Bobby said.
I agree with Bobby as well. Freeport is a fun place to stay. We tied up at the town dock, but it was difficult then to get in touch with the dockmaster. Nice shops/restaurants/bars, etc.
AC to Manasquan Inlet you can take the Intracoastal with no real issues. Sometimes there is pretty aggressive current near the southern inlets, so time the currents. We go from AC to LBI then further north. Will usually stay at Tice's Shoal, and Seaside Heights. The boardwalks are great, but not so enjoyable with COVID. Also, you can stay in Cape May, but if you go a little further up the Intracoastal, Wildwood has an excellent marina. You can rent bikes and take a quick trip to the boardwalk.
About 5 miles north of the Manasquan is Shark River and Shark River Inlet. You can drop in there as well, but after that, there is nothing until Sandy hook. You could do Cape May to AC to Shark River to Sandy Hook/NY Harbor on the outside if the weather is good. The best time is in the morning, so get an early start. The winds tend to pick up in the afternoon and it gets rougher. You can do the Intracoastal from Cape May to AC, but you have to be very careful to stay in the channel. There are some places you can stay on the southern Intracoastal, but we usually do it in one trip from Cape May/Wildwood to AC. It can take 5-6 hours with the no-wake zones. Outside is definitely faster, but the scenery is not as interesting. Once you get up to Sandy Hook area you can anchor in Horseshoe Cove, or go up the Navesink river a bit for some anchorages there.
We've live around Sandy Hook and have been traveling down to Cape May and as far south as Ocean City, MD, up to Lake Champlain, up and down the long island sound, including NY, CT, MA, RI as well as circumnavigating LI. It's a great area to boat. I've even done the Chesapeake, C&D Canal, Delaware River to NYC route, although on a different boat.
Also, Lewes, DE is a nice stop, if you have time.
You are in for a great adventure.