CC at crackers should not be an issue.
I am not sure about OC,
other than that I don't think you will have issues if you stick to the restaurants or bars. The monument is closed so that isn't an issue. the capitol and court house i would stay away from them.
There are no LAWS on carrying in bars or a comedy club downtown. However, the bars will likely restrict firearms on the premesis, but they aint gots to know. I carried at downtown bars last weekend (stayed sober).
Carry concealed. None of the bars or anyplace I'm aware of downtown does patdowns.