Many housing options start opening up in April and into May from graduating medical students and residents, so plenty of housing options are available no matter when you make your decision to come to Michigan. The Admitted Student Slack group is also a great way to hear about housing availability and find roommates.
Many med school students find housing in the White Coat area or Kerrytown, two neighborhoods that are close to the medical campus and have a plenty of rental options.
There are also two co-ed medical societies (Phi Chi and Phi Rho Sigma) that offer some unique housing benefits. The Munger Graduate Residences is a large facility on Central Campus designed specifically for the life/study-style of graduate and professional-level students.
Northwood Community is home to a large multicultural and international population of graduate students, students with families, postdoctoral research fellows, visiting scholars, faculty and staff members.
To explore other options, check out this housing guide produced by VeryApt that features comments and reviews by Michigan Med students, as well as the University of Michigan's Off-Campus Housing Search Tool.