The Mackinaw Club is an 18-hole public golf course in Carp Lake, Michigan, built in 1997 and designed by Jerry Matthews. It sits in the $$ (moderate) price range for golf in Michigan. The season runs Apr 1 to Nov 1. Tee times can be booked 30 days in advance. Guests are welcome.
Details like fees and seasons change, so call the course before you head out.