Most college students go to college within 500 miles (a reasonable one-day drive) of their homes. You can check approximate sources of students for each college from figures published by the college, e.g., "15 percent of our students come from the northeast" or whatever. Usually colleges say this by regions that they make up. The definition of "northeast," for example, may not be the same for all colleges.
For the OP, I'm assuming that if you have a legitimate shot at Yale that the U of Minnesota will be your "safety" college. You should definitely apply to the U as early as possible, to see if you indeed get in. That will be a relief during the rest of the admission process.
You all know about regional college meetings, right?
Fall 2008 Events Where Students Can Meet Admission Officers
Those are good places for meeting out-of-state college officers in your home state.