My daughter attended UM, so I have had the pleasure of experiencing a ton that A2 has to offer. It's a great town and golf there is a treat as well.
If you are working in A2 then there are a host of things to do, see, experience. The UM course is considered "private," and for use by alumni and their guests. If you are in town for an event at the university, that can get you proxy if you are a savvy negotiator. I got on my first time there prior to my daughter attending with somw sweet talking. They may charge you a tad bit more, but you'll get on. Otherwise, a trick I use is to say you are attending some event at the Ross Business School for the week. That should work.
As for the UM course.... It is a McKenzie course full of hills and small greens. It's a fun, fair test of golf. When you're on top of some of the higher elevations you get awesome views of the town of A2 and the university's wonderful architecture. And since you are literally across the street from Michigan Stadium, you see that a fair amount as well.
When in town, you must visit Zingerman's Deli, an authentic NY style deli, unique to A2. The owners are often mention in business magazines for their rich history and wonderful products. And of course you must head to Angelo's for breakfast, right near the UM Hospital System, it is one of those places that can't be missed. And like any university area, simply walking the streets and mingling with the locals has a spirit all it's own.
I miss Ann Arbor a lot. If I can give you any more info send me a PM and I will help you out.