@ehBeth,
I love Chicago and I love California more. I know Los Angeles well, lived there something like 43 years, five in Chicago area in later grammar school. USC is a good school, and, yes, expensive.
The Cal State campuses are also rather good, but there is, last I looked, a crush to get into them as they are having statewide financial challenges. I may not be up to date on the latest on that, and if you two are interested re her going to one of those, do some research.
The city colleges (junior colleges) are often good, Santa Monica being most appreciated, and that college is one of or
the main junior college in the area to send graduates with A.A. degrees to UCLA, a fine university on the west side of town. In my time UCLA was tuition free, but not anymore.
Living around USC is tricky, as a bunch of the area around it is crime addled. My husband went to usc and lived his life until he met me in one very tough part of town, near the university.
I wish you both well, jrice - good fortune and happiness, however it works out.
On convincing her to move - I'm not much of a fan of trying to convince anyone to do anything. It's her life. Try not to manipulate her into a move. She will figure out what she wants to do, now or later on.
You might even end up doing some intermediate thing. She remains in Chicago and experiences life there, you go to USC and experience life there, and see what happens. You will have both tested yourselves in new environments and learned a lot, which is what being eighteen or nineteen is all about.