I can't think of any timeshares in the Detroit area. The place to be, especially in summer, is what we call "Up North" Michigan. Everybody wants to go on I-75 and head north which is where timeshares are and I have not be very successful in getting any trades during summer months. My all time favorite is Traverse City MI and is about a 4 hour drive from Detroit but it is wine country and one of the most beautiful regions you could find in the country. Mario Batali owns a home in northern Michigan in this region and frequently talks about it on The Chew. Along the Lake Michigan shoreline are some really amazing towns. One of the biggest draws in our state is Mackinac Island (accessible by ferry, no cars allowed, only horses) and the Mackinac Bridge (connects the lower and upper peninsulas). My 8 yo DD was just asking me today why she hasn't been to Mackinac Island yet.
In Detroit, it's like any urban city with great sports venues so it would be fun to see the Detroit Tigers, go to Greektown, get some great food and gambling. The Detroit Institute of Arts is beautiful. Not too far of a drive is the Henry Ford Museum in Dearborn and people enjoy visiting Ann Arbor for restaurants and the A2 Art Fair. If you wish to drive further, Frankenmuth is a German town with shopping, horse drawn carriages and famous chicken dinners.
These are just a few ideas depending on how far you want to drive to explore. More information is available at michigan.org