Add to Coldjensen's list:
Entertainment: the Fox Theater.
Sports: a Tigers' baseball game at Comerica Park, a Red Wings' hockey game at Joe Louis Arena, a Pistons' basketball game at the Palace. A Lions' game at Ford Field is not currently recommended.
One-of-a-kind places: the Cranbrook Educational Community in Bloomfield Hills for it's small museums and for its gardens and architechtural gems.
For tours of historical mansions: the Meadowbrook Estate in Rochester Hills, the Henry Ford Estate at Fairlane in Dearborn, the Edsel and Eleanor Ford House in Grosse Pointe Shores.
Local 'downtown' neighborhoods for dining, shopping, and people-watching: Greek Town, Royal Oak, Ferndale, and Birmingham. I'm probably missing some of the other neighborhoods that should be included.
Special Seasonal Events: The Freedom Festival Fireworks on the Detroit Riverfront, the Woodward Dream Cruise along 16 miles of Woodward Avenue in Oakland County.
Skip the Steak-and-Shake, though

. Go to a Sweet Lorraine's in either Southfield, Detroit, or Livonia. Or the Whitney, located on Woodward Avenue in a former lumber baron's mansion.