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University of "Illinois" and "Ohio" State University
To me, the best choice for a college name is after the state the school is in.
The most popular choice is "University of (Name of State)" or "(Name of State) University." In many cases, this is the unofficial college of the state. If you live in Illinois, you want to go to the University of Illinois. If you live in Wisconsin, you want to go to the University of Wisconsin.
The name represents the state. If you are proud of the state you live in, this is the school you want to go to.
The second most popular choice is "(Name of State) University."
In some states, this serves as the unofficial college of the state.
Penn State University is the dream school for quite a few Pennsylvanians (the University of Pennsylvania is a private school). In Ohio, Ohio State is far more popular than Ohio University. In Louisiana, Louisiana State (LSU) is the big one.
In some states, these schools are pretty close to the University of (Name of State).
Michigan State proved at least on the gridiron they are equal to or better than the University of Michigan (and they are clearly better in basketball). Arizona State can rival Arizona (they are in the Phoenix area, while Arizona is in Tucson). Florida State is probably second in Florida to UF, but being second in Florida is not a bad thing.
But in many states, "(Name of State) State University" means it is clearly the second best university in the state.
Kansas State is no Kansas. Oklahoma State is no Oklahoma. Oregon State is no Oregon. In many states, this is the case.
Farther down the list is a school with the state name but a direction (examples include Northern Illinois, Southern Illinois, Eastern Illinois and Western Illinois or Eastern Michigan, Western Michigan, and Central Michigan). None of these schools are even close to the top school(s) in the state. You go to Southern Illinois if you can't get into the University of Illinois.
One exception I would say is Southern California. First, it is a private school. Second, "Southern California" implies the Los Angeles area. I'm sure many LA residents have no problem saying they are from "Southern California." How many people in the southern part of Illinois brag about being in "Southern Illinois?"
A separate category would be schools like "(Name of State) Tech" or "(Name of State) A&M" or any other variation. Georgia Tech is a well respected engineering school. I don't, however, associate Texas Tech with being an engineering school. I know the A&M in Texas A&M is agricultural and mechanical, but that is just a historical reference.