I am always a big proponent of Boston and Savannah, especially if you are interested in history. I think both cities are pretty expensive, but they are fun and very interesting.

Also, if you're really into the Nantucket/Martha's Vineyard thought, take a look at Cape Air. It's a tiny (9 seat) commuter airline, but it's a cool experience. They fly out of white plains NY, JFK sometimes, and Boston a lot.

I will warn you though, I lived in Hyannis for a year. I was too poor to ever get out of that town to see the rest of Cape Cod or the islands so I can't speak to anywhere else. But Hyannis itself is not worth going to. It's super expensive and there is nothing there. I'm sure if I had time and money it would have been a different story.