Just to build on the earlier comments regarding Detroit, et al.
Most of your financial, banking, big corporations are going to be located in the burbs. Troy, Birmingham, West Bloomfield, Bloomfield Hills, and Royal Oak are the richest areas, great neighborhoods, and lots of large businesses (BCG for instance, is located in Troy. McKinsey is in Detroit however.)
Downtown Detroit does have a couple nice areas, like Gross Pointe, and Gross Isle. And the area around Tiger Stadium and the Fox Theatre is very nice.
Ann Arbor as a whole is beautiful. It is a great city, with a huge proportion of the population having college degrees, and more. Like refurb said, it has a liberal feel. Troy, and the cities I mentioned above are about 30-45 minutes from Ann Arbor. But there is NO public transportation that will take you between the two. There is a bus system in Ann Arbor that you can get around on, but other than that, there is zero city-to-city transportation that I know of. A car is a must if you plan to commute.
Hope this helps. If you have any more questions, feel free to ask me. I grew up in Michigan all my life, went to Michigan State, and have spent some significant time in Ann Arbor since my girlfriend went to Michigan. I am happy to help!
~Sam