CDA is pretty good about CC and OC. I have OCd around there for about a year now with no issues to date. I have walked by the CDA PD OCing and they didnt look twice. You should be ok, but there may be a few retailers who get jumpy around OCd guns.
Avoid K-12 schools, courthouses and "secure locations" and you should be good to go.
For lunch go hit up Hudson's on Sherman Ave. in downtown for lunch. Great burgers and a fantastic staff. There is a reason they have been open for over 100 years.