@SeanCo, I have a couple of things that I think are good to consider. I’m going to assume your son has some strong stats, if not strong enough for the Ivies. And it sounds like you are comfortable paying full in-state tuition but don’t want to go dramatically higher. Those are my assumptions anyway.
I would suggest you google “colleges that meet full financial need.” Private schools have very high sticker prices but they also often give significant financial aid. Public schools, on the other hand, don’t often give financial aid to OOS students. So often a private school will cost less than an OOS public, even if the “sticker price” is much higher.
The caveat to that is that a school may calculate that you can pay more than you think is wise or it may include too many loans (though they try to avoid this). Also, there is another thread on CC that points out that these schools may be need aware in admissions and, for example, may give a preference to a student who they calculate can pay $40k per year vs. one who can pay $10k per year, though this varies by school and student. Sometimes they will guarantee meeting almost all, but not all, of need. You can run the Net Price Calculator (NPC) from the school’s admissions website to get an estimate of what the school will cost your family.
The most competitive, wealthiest schools (Harvard and its crowd) are on the lists of schools that meet full financial need. But there are also excellent schools that are more accessible in terms of admissions. Denison is a terrific one and gives lots of merit aid. It has a beautiful campus near Columbus, OH. We liked Dickinson (PA) a lot–also beautiful campus. You mentioned engineering, maybe Franklin and Marshall, which has an engineering partnership. Lehigh is a top engineering science school. Olin is an outstanding engineering upstart. Maybe the University of Richmond, which is in a fun, vibrant city (RVA), with a beautiful campus and nice weather (I hear mixed things about financial aid there, and can’t speak from experience). There are probably others.
Rankings provide only the most general of guidance. How can one compare Reed (a funky little intellectual liberal arts college) and Michigan with 20x the undergrads and Big Ten football), let alone more unique schools? (Newsweek does break out universities and LACs into different categories.) Mine (like everyone’s) would probably not have been accepted to Yale or Penn, but I can tell you they would not have wanted to attend anyway. Terrific schools, obviously, but their environments just would not have fit my kids. Or, maybe one school is #25 and another #55, but #55 has a much better program for what your kid wants to study. Now if my kid was accepted at #25 on some major ranking and #325, and liked both the same, I’d advise they should go to #25. But otherwise, not too much help.
Last bit of long-winded advice: have yours show as much interest in target schools as is possible. Some schools weight this more than others as a factor in admission–they want to feel like a student will enthusiastically attend if accepted (and it increases their yield, which is a factor in rankings). They can sign up for info on the admissions website. You might even get lucky and learn that they are doing an info session in your area, and you can meet a rep. Maybe even interviews. Visit a couple if you can, to see what your kid likes (smaller? larger? urban? small town?). It also shows interest. Some you won’t be able to visit, which is fine.
Also, have your son apply EA if he can–deadlines are fast approaching. It can be helpful in admissions and is non-binding (ED is binding, students must attend if accepted). It’s nice to get a few early acceptances and to get some idea of what kind of aid they might receive. Good luck!