There is a multitude of places to live in and around Detroit, but you have to weigh the pros and cons. You can stay in the city, close to campus, but if you can't afford a place with all the amenities, 24-hour security, off street parking, and all that jazz on your own, then you need to either bunk up with someone or move outside of the city. There are places that are completely affordable for just one person, but you'll probably be making a sacrifice or two. You may have park on the street, or you may not have 24-hour security. It all depends on what is more important to you.
Many students decide to live with other students and can therefore afford to live in some really beautiful places. Detroit has beautiful mansions that have been made affordable since the economic downturn. Landlords rent them out to students and professors alike.