There's not a place on the beach but there are multiple motels on the island that would all be close-ish to this beach. I haven't stayed at any of them, so I'm refraining from making a suggestion.
There are some great places to stay on the island. Hotel Washington is superb but they only have one-bed rooms. We have enjoyed staying at the Tipping Buckets Farm booked through Bread and Water when we have our kids along. Folk Tree Farm through Airbnb is also great. I can't speak for Sunset Resort or Jackson Harbor Resort because they usually book up quickly, but I've heard great things about both.
Places nearby.. none on the beach
They have rental cabins not sure on availability but no hotels on the island itself that we saw. However there are plenty of hotels minutes from the island.
No this beach is on Washington inland the way tip of door county. You take a ferry across to the island.
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