I know Chicago makes transfers complete its core. Chicago's economics department is also very fussy about prerequisites for everything, because it can afford to be. As a result, it would probably take you at least three years, and maybe some summers, too, to graduate from Chicago. And you could have similar issues at Columbia. I am not certain what Columbia does with transfer students and its core curriculum.
What, exactly, are you trying to do? If your goal is to be an international finance lawyer -- just guessing from your screen name -- you would be much, much better served to stay at UIUC, maintain your 4.0 GPA, and spend a lot of time prepping for the LSAT. In the legal world, your undergraduate institution hardly matters, and your law school is everything. Staying where you are would give you a much better chance of getting into a top law school (and probably helps keep your debt down so that you can afford to go to law school).