I lived in Ann Arbor for 5 years in the 80's and still get to the area every other year or so as my wife is from the Detroit area. There are several wonderful things to do and see and the area (except the industrial side of Detroit) is surprisingly beautiful.
Ann Arbor-
!) U of M campus. Park near State St and walk over to the law school (beautiful old buildings with an Ivy League/ Cambridge vibe. Then walk a block north to the "Quad" for a feel of the campus.
2) Outdoors- Visit the Nichols Arboretum and/or Matthael Botanical Gardens -for beautiful forested walks. Also, walk along the Huron River at Fuller Park and feed the ducks.
3) Take a scenic drive along the Huron, just north of town along Huron River Dr.
4) Restaurants- Gandy Dancer- beautiful, old restored train depot housing a fine bar and restaurant- lunch or dinner.
Detroit area-
1) Henry Ford Museum (on Ford HQ campus)- a world class museum highlighting automobiles and the Industrial Revolution in America
2) Greenfield Village- next door to the museum- A CAN'T MISS living, outdoor museum, put together by Henry Ford, who hauled many buildings of historic significance there- including, a fully functional steam-powered machine shop, one of the first Detroit Edison power plants, Edison's lab from Menlo Park, Lincoln's courthouse, the Wright brothers bicycle workshop where they built their airplanes, etc, etc. The park is full of period dressed artisans at work- very interactive. It has a steam locomotive circling the park. This place is amazing! Allow a half day if you have it.
3) Visit downtown Detroit at the "RenCen" (which is GM headquarters) which is along the pedestrian-friendly Detroit River. The area of downtown here is beautiful and safe with nice restaurants and bars.
4) Greektown- Greek bars, restaurants, and a couple of casinos- Think "Little Italy" but Greek.
5) MGM Grand Casino (Detroit's biggest casino). The sports area would be good for the Derby (limited seating during such events- may have to reserve a seat at a price, but can sit at the bar.
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