There is anchoring in the Great salt pond in BI. On the North side. Just as you get in the channel through the jetties, turn to starboard..
Pretty far from the town and dingy docks, but you can find a few spots, but someone will no doubt anchor over your anchor...no biggie unless you want to leave early in the morning. it gets crowed in the anchorage, interesting when the wind turns..Nice to have someone stay with the boat and have a couple of fenders at hand.
If you have a shallow draft there is a second anchorage farther in, still on the north side...tons of Stinkpots there...
45 footer, you should have all chain, it can get iffy when the wind blows from the south. Many boat drag their anchors..
There are a couple of moorings that are right as you enter the pond, by the coast guard station, I can't remember the color, I think Yellow... these are usually left empty and can be used if you get in at night, they will move you in the morning.
You might be able to score a slip at Paynes, it is a "reverse in" type of slip with bare pilings for your bow, can be tricky when the wind blows, actually can be tricky anytime unless you are familiar with backing up in to a slip. Have your bowlines at the stern and lasso the pilings, walk to the bow as the boat backs in
Point Judith is also good for anchoring, the stay can get rough with the ferries' wakes, the north east corner is the best as far as avoiding the ferries' wakes. Those can clear the galley and table in a NY Second!
Cutty Hunk has Mooring balls outside the harbor, most always you can find some empty. They have a tube that stick out of the top, you need to thread your own bowline in there and cleat to the deck, I like redundancy, so I thread two lines in the eye, especially knowing that it gets rough with a north to east wind. Call the Harbor master if you want a slip, dock or mooring inside, might be full if you get there in the afternoon. Food stops serving on the dock pretty early, I think 5:30 or 6...
From there, early in the morning, like 7:00 AM, you can call the Menemsha harbormaster on the phone...(Stillmark Harbormaster I think is the correct town) and see if there is space on the moorings in the harbor. They have 2 mooring balls and raft up to 5 sailboats on those. Also have moorings outside of the harbor, same exposure as Cutty Hunk. Not good anchoring in either place.. Not much to do in Cutty, but Menemsha is the bomb. Active little harbor, very quaint, the buses run all over Martha's Vineyard. Check out Larsen's fishmarket for fresh catch all day.
A couple of restaurants and shops with in walking distance. you can take the dingy in the pond...my personal favorite place to go.
That's as far as I have explored...
This July we make sail for Nantucket Via Cutty, WoodsHole, and Edgartown ...Blue water sail back to Stonington or Pt Judith depending on the weather and wind.
Sounds like a fun trip. Enjoy!