You’ve gotten some good advice so far. With you paying for your own education, I think that looking for full rides from National Merit Finalist status, or academic stats, or swinging-for-the-fences full ride scholarships are your best best.
A school you might want to consider is Ohio State, located in the Ohio state capital and one of the top 20 metros in the U.S. for jobs. You should definitely be accepted, but becoming an Eminence Fellow is going to be the really hard part, but I do think you stand a chance. That would be a full-ride, and Ohio State has a very strong Korean program and also hosts the National East Asian Languages Resource Center.
Another school you might want to consider is U. of Hawaii at Manoa. Honolulu definitely qualifies a bigger city, but looking at its financial aid pages, I’m not sure if they offer any full ride merit scholarships (check with the admissions office). But, it is part of the National Student Exchange program, so this could be a great place to do an exchange as it also has very strong Korean offerings.