If you need a break, the Michigan League and Michigan Union buildings are open and nice places to sit or grab a coffee. The Union has a Sweetwaters (our local coffee chain) and nice couches.
The Observatory is open for drop-in tours (free, led by students) from 12-5 PM on Friday, and hosts events and observatory open-hours (normally free, but pre-registration required) from 8 - 10:30 PM on Fridays. The original equipment is mostly all there, and the observatory has a really cool legacy of early science education.
The whole UM campus is pretty, but the squirrels at the Law Quadrangle are the cutest.