It sounds like your son is doing great! Yes, I agree Texas A&M would be a great choice too, unless the environment is just not a good fit.
The answer is very family/student specific, since the complete application package is very important for merit aid and the family financial picture very important for need-based aid. You can’t look at just the “sticker price.” What students pay varies greatly, in some ways like airfare pricing. For example, Case Western Reserve U. (CWRU, “Crew”) is an outstanding STEM university in Cleveland, with a medical school and research hospital immediately adjacent to campus. It has a high sticker price, but a high % of students receive significant merit aid, which can often bring the price down to more like $30k to $45k per year. But it varies greatly.
You can google colleges that meet full financial need. Things to keep in mind. They might calculate your contribution at more than you feel comfortable paying. Or, they might be “need aware,” and it might be more difficult for a student who requires a lot of aid to get a yes from admissions. But, at least there is a commitment and a claim to meet full need.
Google Miami of Ohio merit aid for a very simple chart showing merit aid eligibility by grades/test scores. The school, which is excellent has engineering. This is a good example of a way to find out what amount of aid your son might anticipate. Some excellent public schools offer similarly concise descriptions of merit aid by grades/test scores. I’m thinking of Kansas, KSU, Iowa, Iowa State, Nebraska, Alabama, etc. (KU and KSU are in great college towns!)
If your son is hands-on and project-oriented, check out WPI in Worcester, MA. It’s a mid-size national STEM university with a beautiful campus in a nice area of Worcester. It is notably hands-on and project-oriented. Students take 3 classes at a time and do lots of internships, etc. It’s not well known in TX, but students have some of the highest starting salaries of any school. It’s done well in admissions and attracts very excellent students.
Last tip: having gone through this 3 times, I’d suggest focusing more on fun and learning what’s a good fit and less on where one can get accepted. Is an urban school better? Would a University of Alabama, with big-time football, and all that be better for your son, or a CWRU or WPI, where the vast majority of students are STEM majors and sports are an important part of the culture but not so big-time? Would Colorado School of Mines, with the Rockies and lots of outdoor opportunities be better?
Exploring a little can take the edge off too. Say WPI looked like a great fit. You all wanted to see it and arranged a trip up that way, with trips to other excellent schools like Rochester, RIT, RPI, etc. Well, if possible, allow a day in the middle just to visit the Berkshires or Boston or some other area of interest while you are there. We always stayed positive and tried to explore a bit and have lots of great memories of those trips. For example, we visited several Midwest schools with one of ours. We took a day off to visit Frank Lloyd Wright’s Taliesin home and do a beer and pizza trip on Lake Mendota in Madison, WI. Made it feel more like a vacation than a slog.
Last, last tip: If you do decide to visit more than a couple of OOS schools, take notes–tour guide’s name, info session host’s name, important pro and cons FOR YOUR SON, and just funny, offbeat things that happen. Those can really jog the memory later.
Good luck, have fun!