I'm also applying to grad schools, and no way am I applying to Detroit. Never been there, but one of the most dangerous cities (if not, the most dangerous city) in the nation. I'm thinking around the New York/New Jersey area, or the Southwest.
Lived in Michigan until two years ago. Avoid Detroit at all costs. That city has been slowly dying now for about 30 years. Might I suggest The University of Boulder if that is an option. Great and interesting city plus you are only about a 25 minute drive from Denver. When you need a bit of a break a ten minute ride and you are up in the mountains surrounded by wilderness.