In addition to the fine suggestions already made, there is also the reality that today's American car industry is still very much SE Michigan-based. Have thrown together a quick map of the some of the key sites. Unfortunately you need an employee badge to get in to most of these places. However, driving by the tech centers will give you a glimpse of the enormity that exists. The proving grounds are harder to see, best to simply pull up Google maps and look at satellite view.
Ford's product development/tech center buildings are easy to see, simply drive down Oakwood Ave between Michigan Ave. and Rotunda. Greenfield Village and "The Henry Ford" (the indoor museum part of what was formerly called Greenfield Village) are in the middle of it all. World Headquarters in on Michigan Ave.; near them, Ford's marketing and other non-engineering buildings.
GM's product development centers are many. Powertrain is in Pontiac but I am not sure where, have never been there. Vehicle product development is at Warren Tech Center shown on map, between 12 and 13 Mile Rd and between Mound Rd. and Van Dyke. It's a huge campus. If you drive north on Mound from I-696 and look to right, will see the famous Design Center dome and huge reflecting pool. If lucky you will also see the several dozen fountains shooting a wall of water up dozens of feet. Quite a spectacular site.
Chrysler's tech center is more contained, can be seen from local roads around it and from I-75.
Toyota has two tech centers, the smaller one shown on map, the larger, newer one just off the bottom of map, south of Ann Arbor.
Nissan does engineering work in Farmington, not sure exactly where it is.
All of this is just to remind that the auto industry is very much alive in Detroit Metro. If you ever get a chance to see the mid-August Woodward Dream Cruise you will see the handiwork of thousands of current and former auto industry folks, their beautiful cars an extension of the "hobby" they work in every day, or used to.
I was remiss in not pointing out GM's Renaissance Center downtown. Marketing and Onstar are there as are the high level execs. There are always new GM cars on display inside, which is open to the public. Look for three large skyscrapers nestled together along the waterfront.
In addition, the entire Metro area is filled with smaller tech centers and countless suppliers big and small. Work starts early every day, the roads busy before 6 am, hourly folks heading to or from their shift, salaried folks rushing to the office or conference room to join coworkers in a global call with counterparts in China, Europe, Korea, Australia and other locations. It is truly an international city, and it is all about cars.