Another note on out-of-state public schools: in addition to their acceptance rates for non-residents, take a good hard look at the tuition discrepancy between in-state and out-of-state, and find out if you would qualify for state residency after one year of living there as a student (some states allow it, others don't). For example, I was all set to apply to Univ. of Colorado (I'm a CA resident) until I found out the out-of-state tuition is something like $60,000! Also be aware that a lot of state schools will waitlist out-of-staters initially. Unless you are really enthusiastic about going to one of them, it might be a waste of money in many cases since you'll likely get into other, private schools first. (there are some state schools, however, who end up taking lots of non-residents, like UVM.)
But definitely apply to your own state schools!!!