Please note that it is not “schools” that are accredited, it is individual degrees at the school. Post #32 mentions Texas A&M Corpus Christi. The included link is to the accredited BS in Mechanical Engineering. However, the BS in Electrical Engineering does not appear as an accredited degree on the ABET site.
http://main.abet.org/aps/accreditedprogramsearch.aspx
Colorado Mesa does not appear to have any ABET accredited degrees.
In line with the numbers that @ucbalumnus, neither Arizona nor Arizona State are going to be within the budget stated for an OOS student without substantial merit aid not likely with an 25 ACT, and they are both on the order of the same size of UT Austin.