Are your kids medium-level students, or are they high achievers?
If they're high achievers, when the time comes you should look into selective private colleges. There's the top tier - Harvard, Princeton, etc. - but are also many excellent colleges that are a tiny bit less known but that offer superb educations and that give substantial financial aid, often making the price lower than attending a state university. I'm thinking of places such as Hamilton, Wesleyan, Franklin & Marshall, Earlham, Haverford, Oberlin, etc. They also typically do care about geographical diversity, and someone from Wyoming will have the edge over another east-coast applicant, all other things being equal.
There are also similar colleges for medium-level students, such as Bradley University et al. They often have less money than the selective colleges, but they're still worth a shot.
But you're leaving out an important factor - which colleges are a good fit for your children. If the kid and the college aren't a good match, the kid is much more likely to do poorly, drop out, etc. And that's worse than paying a little bit of extra money to make sure the kid goes to the place that provides the biggest bargain. I work in higher education and I see this all the time. Things like small student body vs. big student body, academic orientation vs. more laid-back party orientation, urban or suburban or rural, diversity or homogeneity, campus atmosphere and ethos, supportiveness, resources for students facing challenges, good departments in the field the student is interested in - these matter as much as whether the student gets a full ride.
