There are a ton of small communities that lie within 30 minutes of Zville, but hardly any of them will be diverse. It's in Southeastern Ohio which is not a diverse area at all, and people are not used to diversity. The population of Zanesville is about 10% African American, and any small surrounding towns will be less than 2%. Your best bet is to live in Zanesville itself, probably closer to the north side near the Colony Square mall. But it might also be nice to live near your work and not have to drive through Zville, which is a pretty long drive. There are nice areas scattered throughout. The best thing to do is just visit for a weekend and look around. Nice areas will look nice and bad areas will look bad.
When I still lived in Ohio, the downtown area was not the nicest, try to avoid living downtown. It was run down and known for drugs. I worked downtown and my car was broken into. But the cops were always quick to hand out parking tickets.
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