It seems you might be able to spend a week in a Caribbean resort for less cost than many mainland U.S. resort areas like New Jersey or Cape Cod.
Otherwise, I suggest Martha's Vineyard instead of mainland Cape Cod. I've spent quite a bit of time on MV and find it very nice and relaxing, unless you're staying in or too close to Edgartown area which is good for a visit/stroll but too crowded for my taste. Since I know the people who own it, I've stayed at this specific place many times; it's private, beautiful, peaceful, romantic...all those good things:
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