McMillan is a very busy street, so you may want to consider the noise factor. It's one way and multi lane.
If you wanted to walk over to the Corryville Kroger's, it will take you about ten minutes. Is that a safe walk? Well, it's urban Cincinnati, so you can get mugged anywhere. I used to walk all over Mt. Auburn and Corryville at night and I never had a problem. But I lived there a while and I knew the neighborhood and how to avoid trouble. Since you'd be on a major street, you should be fine by walking up McMillan to Auburn, then over to Kroger's.
And I don't think it is particularly unsafe to walk from those apartments to campus, which is not too much further than the Kroger's. You just need to pick your times. I'd be more careful later at night, for sure, but that's just sound advice in the city.