In Boston is the USS Constitution, not technically a museum ship, but a must visit if you’re in the area. Flagship of the Greatest Navy in the history of the World. The current US Navy.
In New London Connecticut is the USS Nautilus and Submarine Force Museum. Pretty good one to visit. Close to Mystic Seaport and all the attractions there.
Mystic Seaport has a bunch of boats and is a seaport museum. This might be the best place to learn about historic boat building in the US.
USS Intrepid in NYC on the Hudson is incredible. I highly recommend it. It is sea, air and space. Includes the Space Shuttle Enterprise, usually there is a non-nuke sub next to her. The Intrepid served in WWII. One of the 24 Essex class carriers. She also did recovery in the 60s into the 70s for NASA missions.
South Street Sea Port on the East River in NYC is also a good place to visit. I think they still offer tours of the Wavertree, one of the largest sailing ships built. The old Ambrose Light Ship is also there. I think the China Sea has moved on, but not sure. I think many tall ships have called South Street Seaport home for a time and then moved on, I’m not honestly sure how that works.
Tuckerton Seaport & Baymen’s Museum on the Atlantic Coast of New Jersey has some wooden boats but not ships. Very nice museum though. Includes a boat, The Adam Hyler, that I use to skipper and ran the maintenance on for years.
The Battleship New Jersey in Camden, New Jersey. The most decorated ship in US History. A great museum ship. Can look for the Fish & Ships deal that gets you onto the New Jersey and into the nearby Aquarium. I served in a combined fleet with the New Jersey one sea period. It is probably the greatest Battleship in the history of the world.
(Please note, the USS Enterprise CV-6 was the most decorated ship in WWII and perhaps the most important ship in Navy History, but she was decommission and turned to scrap very sadly.)
USS Constellation in Baltimore is a fairly good museum ship. The ship is of no actual historic importance, it is not one of the original Frigates. This is an 1854 warship named for the famous Frigate. The Inner Harbor also has the Lightship Chesapeake, a Coast Guard Cutter and a submarine. They use to have a destroyer, not sure what happened to it.
I think that is all my museum ships. I might have missed one or two.
Two on my list to go see:
USS Yorktown CV-10, very near Charleston, SC. Another Essex class carrier, named for CV-5 sunk at Midway. I hear it is great.
In Philly, across the Delaware from the New Jersey is USS Olympia and sub, Becuna. The Olympia is the last ship of the Great White Fleet and was for a time the flagship of said. It was also the flagship of Commodore Dewey at the Battle of Manila Bay in 1898. It is open for ship tours again.