Draw a line, east to west, from Grand Haven to Grand Rapids, east to Clare and Lake Huron. The farther you travel north of this line, the better the grouse hunting, both in access and opportunity. Southern Michigan deer hunting-Jackson,Calhoun, Washtenhaw counties offer the best. Saginaw Bay, Shiawassee, Lake St. Clair marshes offer good duck and goose hunting.
I am not a fan of urban blight areas.
I would encourage you to look at Grand Rapids area up to Muskegon, fewer people, less crime, better outdoor access for hunting and fishing. There is a migration corridor that swings through Michigan from Ludington south to South Haven for ducks. East of Grand Rapids you can get into Southern James Bay origin Canadas. Mississippi Valley flock "splits" on Lake Michigan, moving down the coasts southward during fall migrations. Giant Canadas abound in south central Michigan, offering late season hunting season annually.