I was amazed to learn about all of the history in the city. A visit to the Alhóndiga is helpful to start to understand the beginnings of the revolution against Spain. I went on a regional tour that took us to the church in Dolores Hidalgo where the "cry (gritó)for independence" was made, and nearby town square more people were rallied.
Muralist Diego Rivera was born in Guanajuato city and there is a museum of his childhood home.
The rivers /streams used to be tunneled under the town but now they are used for traffic. I recommend taking a local bus that goes through one of these tunnels just to get a feel. I recall some buses had to make multi point turns to deal with the tight quarters of the tunnels.
Try walking the downtown streets for 15 or 20 minutes without any map or GPS. See if you can find your way back – but keep a map or phone with google maps in your pocket when you fail.
Oddly, I never got around to visiting the mummy museum, but if you like curiosities it gets good reviews.