Here it's what I would do if I was visiting Michigan for 15 days: 1. If you want to do boating, head to the waters of Lake Michigan or Warren Dunes State Park, which is not too far from Chicago. 2. Spend 1-2 days in Saugatuck riding the sand dunes 3. Head to south of Detroit to visit the Henry Ford Museum and Greenfield Village and the Detroit Institute of Arts might be worth your while 4. Spend 2 nights in Sleeping Bear Sand Dunes National Lakeshore 5. Explore the quaint towns of Charlevoix and Petoskey (ski nearby Nubs Nob)
Great suggestions., just make sure you visit Michigan in the summer because right now winter there is crazy with low temps and snow. Summer is much better time to explore the state for the beaches too like Weko Beach which is the most beautiful stretch of Lake Michigan beach.
Mackinac Island is a must and so is the Dunes and the upper peninsula. when i was there i got to walk along Mackinac bridge, which is once a year on Labor Day is opened to foot traffic. It's very eerie walking over this very large bridge but totally worth it.