At University of New Mexico, you’d be competitive for the Regents Scholarship (Full tuition plus full room & board)
This is a competitive scholarship with applications due December 1.
Also at UNM, you would be guaranteed the Amigo Scholarship (OOS tuition reduction) that would put your COA at ~$17K.
https://scholarship.unm.edu/scholarships/non-resident.html
UNM has good physics & EE depts (ask me about the physics dept–D1 is a UNM physics grad). NM is home to 2 National Research Labs (Sandia and Los Alamos) and 2 military research labs (Phillips Air Force Research Lab in Albuquerque and White Sands in Alamogordo). Plus Intel has major facility in town. Lots of internship possibilities.
Another possibility would be NM Tech–small engineering college in Socorro, NM (which shares its campus and facilities with National Radio Astronomy Observatory if you’re into astronomy or astrophysics. The Tech students have their own student-run radio telescope.) Tech offers OOS tuition remission (Tech’s tuition, fees plus room & board ~$14K annually) and several levels of scholarships. You’d qualify for the Presidential Scholarship which is $4K annually, putting your costs at about $10/year.
http://www.nmt.edu/scholarships-financial-aid/50-financial-aid/financial-aid/181-scholarships-for-entering-freshman
http://www.nmt.edu/scholarships-financial-aid/50-financial-aid/financial-aid/183-scholarships-a-tuition-reduction-programs-for-non-residents