The historic Detroit Observatory, on the corner Ann and Observatory streets in Ann Arbor, is owned by U-M and run by the Bentley Historical Library. They host open houses on select Sundays where you can tour the building and chat with the docents about the building and its history, both as a foundation for UM and as a part of Ann Arbor.
The Astronomy Department collaborates with Bentley to host public viewing nights. Viewing Nights are weather permitting only. Please also note this historic structure pre-dates elevators, so you must be able to climb stairs to get to the dome and telescope.
Check the calendar or Facebook page (both shown below) for events. Weather updates for viewing nights are done around 5 PM on the day of a viewing night.