...at The Grand Hotel on Mackinac Island. Also there's Wawashkamo...if you want to play a 19th century links course (though those take a ferry and horse-drawn carriage ride).
Things to do? Fishing/Boating on big lake or interior lakes (Torch, Charlevoix). Wineries and restaurants up Leelanau peninsula. Hiking at Sleeping Bear Dunes National Lake Shore, Boyne, or up across the Straits of Mackinac on the UP at Hiawatha National Forest. Tahquamenon Falls is a little further and magnificent. Pictured Rocks Lakeshore on Superior is also great, but more of a commitment.
My mother lives up in that area. If you actually considered it, I could tell you everywhere you should hit for dining in that region.
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