Welcome to Detroit from a proud resident! Hope you enjoyed the fine [December] weather this weekend. I actually just returned from Greenfield Village for their Christmas event 'Holiday Nights'.
If you are still around, I HIGHLY suggest you head to Dearborn and get some Arab food. Detroit metro has the highest number of Arabs anywhere outside the Arab world and some great food from the region. Eat at Al-Saha on Warren Avenue (everything is good), then go next door (you'll see it) to Shatila for the best, and cheapest, Arab dessert you'll ever enjoy. You'll need to take a number from the door on the far side from Al-Saha.
Hit the Arab American National Museum just a mile south to learn about the history of Arab immigration to the US and some cool stuff about Arab history/culture.
The famous Rouge River Ford factory is another mile south from there- worth seeing from the outside (it used to employ 100,000 people, yes, 100k), but they do a great tour too.
Get coffee in midtown Detroit at Great Lakes and take it to the Detroit Institute of Arts- literally one of the best Museums in the US.
The main roundabout downtown- campus martius- has an outdoor skating rink and some super cool Christmas decorations now. Worth walking around if not skating as well!
The largest historic public market district is in Detroit- and its super cool. You missed the Saturday market, but for others that come, definitely grab a coffee at Germack coffee (local roaster in the market) and walk around the Eastern Market, get some local produce, eat some fresh basked goods, and enjoy the eclectic scene (
http://www.detroiteasternmarket.com).
Detroit certainly has a crime problem, but the downtown and trendy Midtown areas are just as safe as most downtowns. Do not worry about walking around there, even at night. Take the same precautions you would elsewhere in the US.
Hope you enjoyed the time you had here!