No CC inside gov't buildings, but on gov't property is okay. OC inside gov't buildings is okay unless previously banned by law (such as courthouses and police stations).
However, as there is a blunder in the law concerning what should be on official signs banning guns in those places, many people believe that OC is not allowed in gov't buildings either. Legally, it is, but you may run into resistance with the uneducated.
The Zoo is owned by the city, so CC in their buildings will be off-limits, but the Park itself is fine.
I've generally had no issues with OC in Cincy, ranging from banks to restaurants to stores.
Enjoy your stay! If you want a good breakfast, check out the First Watch downtown on 7th. I've OC'ed in there several times, including in front of LEOs, without any issues.