Happy for you. Sailing is a lifelong gift.
I am not sure anchoring is allowed in Napeague anymore.
Years ago, I looked in to it, and discovered that it is a No Anchorage harbor.
Perhaps it has changed, I do not know.
Some other places to consider are the harbors on Shelter Island.
Also, this year we anchored one night in Northwest Harbor, east of the Cedar Island Lighthouse. No protection from the SW, but it was a calm day, so it was fine. Rowed ashore, walked the beach, checked out the lighthouse etc.
IIRC, the harbor was "protected shellfish beds", and that was the reason no anchoring was allowed.I'd point out, that if the waters are US navigable waters, they are likely not allowed to make them a "no anchoring zone". It would violate federal law IIRC.