This is the fault of people where you live. University of Illinois is a very well-known top-ranked school. If certain pockets of Ohio have never even heard of it, that just means that they’re provincial and out-of-touch. And it’s probably not the kind of place the OP would want to live anyway, since they say they’re interested in moving to Chicago.
Having said that, it’s advantageous to get an undergrad degree in one place and a graduate degree from the other. It makes you look more well-rounded (and like you didn’t get into a grad program just because you knew someone).
