My alma mater, Case Western Reserve (no, it's not a military school--it just has a stupid name), has some solid engineering programs, though its real strength is biomedical. The ratio of men to women is about 3:2, and probably even more skewed in the engineering school, though the breakdown changes by program. (Chemical and biomedical engineering seem to be more even than, say, mechanical or computer science.) There are certainly women in all of them, though. There are also plenty of campus organizations for women in STEM fields.

It's private, but has in the past been pretty generous with scholarships and financial aid.