Considering that the cops in Ohio are some of the MOST anti gun cops I have ever seen I can't understand why anyone would choose to go in there with a sidearm. Some of them couldn't care less if you have a permit or not. They don't believe "citizens" should have guns even if the law says it's OK. Illinois is about the same. I lived in Illinois for 12 years and today I will gladly drive all the way around that State rather than go through it. And I have several times.
As with any other State, I'm sure it depends on where you are. I know there are some Cincinnati MPD who think that way (and live on in YouTube infamy) - and then there's the jackwagon who is (was?) the Hamilton County sheriff - but my experience in both Butler and Clermont counties, as a then-resident CCW holder, was completely different.
If I'm still at my current client in another month and a half, I suppose I may get the chance to find out how the LEO in Miami and Shelby counties are - though that would likely require interactions with them that don't normally happen (since I don't speed or otherwise draw attention to myself).