Not specific to where you are staying, but the Mid-Cape Athletic Club on White's Path, in South Yarmouth has indoor tennis. I think Chatham Light is open some days around the end of December, not sure if it's the same tour as in the summer. Also, not as grand, but the Three Sisters you can walk up to anytime. Race Point visitor's center is worth a look, you might be able to get to the life saving station. Provincetown is sort of nice, uncrowded this time of year (as many towns out that way are), try the Public Library and see the scale model (66 feet long) of the Dorothea Rose schooner, pretty cool.
Restaurants, not all that sure about that.
Wish I was going then!
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