Wyoming's posted price is 22k annually before aid- that's not much better than Minnesota's 30k.
Your best bet is going to be merit scholarships if you're looking at a certain price point. The first option is to find independent grants and scholarships online that will often need you to meet certain reqs ( based on your background, you being an international student, looking to pursue a degree in engineering etc ) and will have you write an essay to apply. They might offer a few thousand dollars each, which will help you significantly.
Your second option for merit is applying to colleges with lower stats than yours. If you get mostly As and Bs, look for schools with students who mostly get Cs and Ds. These universities genuinely want you to attend- youll boost their stats, and they are often willing to grant thousands in scholarship to get you to attend their school.
Kind of going along with the prior, many schools also have Honors programs or certain degree combinations which are eligible for financial aid. You need to look into this now as admissions is open right now, and many schools require an interview or separate application to these programs.
Let me know if you want any links to scholarship opportunities, or if you're having a hard time finding universities or programs that follow the above. The US process is a lot different to the process in the UK, it can be very confusing.
edit- minnesota has
int. scholarship plus
honors scholarship. Theoretically, if you applied for and got both, you would cut the cost in half.