Princeton/MIT-like schools with merit scholarships?

Case Western! Last year their general merit scholarships topped out in the low 30s. There are also a very few full tuition awards by separate application. Had my daughter gone there, our costs would have been in the low 30s. Great school, it ended up being her second choice. STEM is strong there but it’s not just a tech school. There are no barriers to majors once you are accepted (for example, switching from CS to engineering).

Wash U is also worth a look - merit scholarships also by separate application - very tough to get but worth a shot.