I'm a fan of Nantucket. Essentially, the entire town is accessible from the
dinghy dock. Nantucket moorings must have over 100 well maintained moorings. You're not likely to get a slip this time of year, if you haven't already reserved it, but maybe. You can walk to Jetties Beach, if that's your thing. More shops, restaurants, etc than you could handle. The Whaling Museum is fun. People or yacht watching on Long Warf, etc. Or rent bikes or mopeds (also right in town) and explore the island. You can rent kayaks or paddleboards just south of town in the harbor as well.
I also like the Vineyard, but there are several towns, so its hard to take it all in. We prefer Edgartown, but there are limited moorings that are heavily booked this time of year. They do have an online reservations system. Vineyard Haven is okay, particularly for the day. The moorings outside the breakwater are rough in northerly winds and there is an anchorage out there as well. You can take a cab from town to town, but it gets expensive. Oaks Bluff has few places to moor or
anchor, so I would not start there. Here's my all to generalized recap of MV towns. Edgartown - quaint, Oaks Bluff - tshirts and beer, Vineyard Haven - dry town (though they can serve beer or wine with food now)
Have fun.