By "Detroit" do you mean actually in the city or one of the suburbs? Since anyone who could afford to moved out of the city 40 years ago, there's might actually be more to do without going into the city itself, depending which area you're at. In the city, I highly recommend Opus One. The Whitney is in this cool old mansion, but I wasn't particularly impressed with the food. Go see a DSO concert at Orchestra Hall; the orchestra is good enough to attract the likes of Jarvi and Slatkin as music directors, and the hall is one of the best in the world acoustically. The DIA (art museum) is also very good. Outside the city, check out Birmingham, Royal Oak, and Ann Arbor. Just across the Detroit river is Windsor, Ontario, which is much safer and cleaner than Detroit. Just make sure you avoid the roving gangs of drunk 19-year-old Americans.

For a good weekend trip you can drive to Toronto in about 4 hours, or Chicago in 5-6. As for shopping, it depends what you are looking for, suits, streetwear, vintage, etc.