The "most phallic" building in the world, apparently, according to readers of Cabinet magazine in 2003: the water tower in Ypsilanti, at the corner of Cross and Washtenaw, also locally called the "brick dick" or the "aquacock".
The Chelsea Milling Company, manufacturers of nationally-beloved "Jiffy" Mix baking mixes since 1930, is located in Chelsea. You can call ahead to schedule a tour of their facilities.
Attend a movie, play, concert or comedy show at one of the many venues in Ann Arbor. Alternatively, actor Jeff Daniels has established a popular not-for-profit professional theatre, the Purple Rose, in his hometown of Chelsea.
The original Borders bookstore is in downtown Ann Arbor, a town known for its high bookstore-per-capita ratio.
Literally every town and village in the area has a quaint downtown area with pleasant dining and shopping. Ann Arbor's is by far the largest, but if you don't have time to meander through the entire county to see all the others, you should at least be sure to check out the historic Depot Town in Ypsilanti.
If you like to drive, there are some scenic paths along back roads in the county, particularly Huron River Drive between Ann Arbor and Dexter, which unsurprisingly follows the banks of the Huron River.