They do, and it's incredible. The only downside was that its business hours are our business hours: 9-5 during the week. This meant taking a vacation day to check it out. However, we had our own personal tour guide and were able to see the entirety of the building, including the mayor's office.
I learned a lot about Cincinnati's history and politics on this tour. I was also impressed to see how much artwork was all over the building, especially in the forms of stained glass and painted frescoes. Even if you're not into the political side, I'd highly recommend taking the tour just to hear about why each stained glass scene was included, what the characters represented to the designers, why art was infused throughout a governmental building.
A few photos to pique your interest:
By the way, City Hall was built like a fortress because citizens set fire to the previous City Hall. Most of this building is marble or granite... a bit harder to burn to the ground.
Our tour was over an hour long, completely free, and all of our questions were answered. Our tour guide was knowledgeable and nice, and the building is fascinating. (If you go, see if you can request William Dreyer.)
City Hall's tour information: http://www.cincinnati-oh.gov/council/pages/-10585-/
More photos from our trip: http://www.flickr.com/photos/rrrrred/sets/72157622647357217/
