All you have to do to earn the Detroit Motor City foursquare badge is like foursquare Cities on foursquare and then check in to five venues on a yet-to-be-posted recommended venue list (more than likely the most popular and obvious venues in the city).
You will then earn your shiny new badge and see the following message:
Hangin’ in The D, huh? From technicolor airports to Model Ts and The Temptations, it’s a pretty swell city. Nom a coney dog with everything, then scream your head off at a Red Wings game — you’ll fit right in.