Detroit is often blighted and bizarre. It's very DIY. It's cool, if you like that sort of thing.
Go to the Motown Museum. Seriously. It's the old Motown recording studio(plus offices, etc). Amazingly, it's still there. And - this part is very Detroit - basically it's almost like it was. They just stuck a museum sign in front of it. Complete with the gear, echo chamber (in the attic!). You wont regret it.
Daytime: visit Eastern Market (enormous farmer's market, go on market day for incredible people watching and the occasional busker). While there, eat an amazing breakfast (or lunch) at Russell St. Deli (mmm, bacon). Then go next door to Rocky's and buy some bulk candy for dessert.
Or catch the Tigers play at Comerica Park. It's a great new ballpark, with some amazing views of the city skyline. Then go for a walk and poke around Bricktown and Greektown.
At night - check out interesting local bands at Majestic/Magic Stick (bigger venue) or Lager House (smaller venue - while you're there, cut across the street at see the ghost of the old Michigan Central Depot - huge old train station, people sneak in and take amazing pictures).
Eat at Union Street (across from the Magic Stick). Great city scene.
Shopping: hit Gratiot Ave. for the local pawn shops. It's hit and miss. If you like thrifting, there's a huge Salvation Army over in Corktown. If you like architecture, just drive around downtown and marvel at the old abandoned buildings. Check out "the fabulous ruins of detroit" and make your own walking/driving tour (yes it's true the old model t plant is abandoned and you can see it up close if your careful):
http://www.detroityes.com
That should get you started....!
Aj
P.S. Events calendar and local press here:
http://www.metrotimes.com