When you say anchorage, are you being literal? No moorings? That would not be terribly limiting, but maybe a little.
Newport is probably a must. It can get busy, but its all about boating, so its fun to be part of the scene. There is a designated anchorage.
Block is a must as well. There is a huge anchorage, but the 20ft depths often go first and the closer to the channel you are the closer to 40ish feet is common. Have lots of rode.
You can anchor in West Harbor at Fishers Island. Its very quiet, quaint and little to do. Only one restaurant. The marina (nor island culture in genernal) doesn't exist to cater to tourism, but won't turn you away either. Just don't expect a 5 star experience and go about your business.
I'm not sure there is anyplace convenient to anchor at Mystic, but I would put it on my top 5 anyway. I've been to the seaport many times (although not in years) and I want to go back. A slip at the Seaport includes your access to the grounds. Good deal.
Its certainly possible that weather will cause you to want to spend more time in Narragansett Bay. Open water between Cutty and Block is typically fine, but can get pretty rough too.
If you head up the Bay, I would make Bristol a destination. Lots of boats were originally manufactured there. Large anchorage just south of the mooring field. Soft mud, easy to set, not the best holding, but winds are not typically all that tough that far north. The Hereshoff museum has moorings too, but they are exposed and rolly.
Both Potters and Dutch Harbor, mentioned above, are excellent large anchorages.
I was not a huge fan of Greenport or Shelter Island. Sag is worth seeing, maybe. It's sort of Vineyard-Nantucket-ish. Three Mile Harbor is a great anchorage and three miles from East Hampton. Although, the Hamptons are not worth it, IMO. They are strictly intended for that that are into conspicuous consumption.
You asked for a cruising resource. I like this one: