I think a lot of times, "strong STEM programs" in the public perception is equated with "big research university" which leads to oxymoron when looking for PUI for STEM.
Loyola Marymount University, in LA, fits the description. The STEM program wasn't the most competitive out there (but that's in comparison to nearby schools like UCLA, Cal Poly, etc), but the teaching quality was top-notch and there was a pretty direct pipeline from the engineering school to the big aerospace/defense contractors in the surrounding area.
I don't know anybody from any of my programs who isn't either gainfully employed in their field of study, or at some competitive grad school, and we graduated in the middle of COVID.
Of course it seems to be in a competition with USC to be the most expensive stickerprice university in the country, but the dirty little secret of private schools is that almost no one pays that price. To keep diversity up they shower disadvantaged students with scholarships, to keep academic standards up they shower academically competitive students with scholarships, and that's all paid for by charging the obscenely rich an elevated tuition, who in exchange are put in a situation where they're rubbing shoulders with a mix of talented students and a much higher than average concentration of other rich kids, leading to networking opportunities for everyone involved.