Those seem like three great choices for you - I don’t think you could go wrong with any of them. They’re all solid in your core academic areas of interest; you’ll just have to figure out which fits the best across the board. Areas you might want to compare:
Most popular majors. Finance is #1 at Lehigh, followed by MechE and CS… there are pluses and minuses to being in the most in-demand major. (“Critical mass” is nice, but are there enough internships, etc. to go around?) Business and management top the list at W&M, followed by psych, econ and poli sci. At Rochester, Econ is #3 and Business is #7, with the other top majors being health/bio, math, psych, and music, and then CS/Engineering.
Course offerings in non-major areas of interest. (i.e. How much do you value a “cluster” in Japanese Pop Culture… do you want to study photography, graphic design, etc?.. are there other “niche” subjects that interest you, that are better represented at one school than the others?)
Gen Ed requirements, core curriculum, and/or flexibility of the curriculum. (When you map out your hypothetical program, how much time do you have to spend on requirements you wouldn’t take unless you had to?)
Greek life: All three schools have fraternities and sororities, but from what I understand, Greek life is probably most central to social life in general at Lehigh, followed by W&M, and the least so at Rochester. But look into this, in the light of your particular interest, or lack thereof, in joining a fraternity.
Campus culture - the relative prominence of the arts, athletics, politics, and other ways people invest their time and energy. What do people do for fun?
Weather, walkability/public transit (do you expect to have a car at college?), nearby cultural and recreational opportunities.
Diversity - do you care about the demographic differences? Also economic diversity. (It’s interesting to me that the public U has the highest median family income of the three!)
https://www.nytimes.com/interactive/projects/college-mobility/lehigh-university
https://www.nytimes.com/interactive/projects/college-mobility/university-of-rochester
https://www.nytimes.com/interactive/projects/college-mobility/college-of-william-mary
Are they connected where you hope to get internships and jobs? (For example, W&M would probably be better than the others for DC connections)
How much of an “ED bump” does each one give, and do they have EDII? (I think Lehigh and W&M have EDII but Rochester doesn’t.)
I have toured Rochester (hands-down the most informative info session I ever went to with either of my kids) and also have known several kids who have loved it there; and I know W&M from attending summer programs there as a teen (when dinosaurs roamed Colonial Williamsburg) but I have never been to Lehigh or known anyone who went there. My impression is that it’s more of a “love it or hate it” place than some others (maybe a little like Claremont McKenna in that way?) - the trick is to figure out whether you’d be in the “love it” group or not. (The complaints I have heard have been along the lines of “You’d better love Greek life 'cause that’s all there is to do,” but I’m sure there will be others who will rebut that.) They’re all truly excellent schools, with a lot of overlap - which goes to show that you’ve figured out what you want and you’ve identified a group of schools that has those priorities in common.
One quirk of Rochester’s, BTW, is that they solicit a Parent Recommendation… so if you decide to ED there, give your folks a heads-up about that! (I didn’t think it was important when my daughter applied, but then they started sending reminders and I relented, lol.) They also ask a bunch of questions about which on-campus activities/clubs/etc. you are interested in, so that you have to actually look them up and rank your favorites. The more you show that you’ve really investigated the school and thought about how you’d want to participate in stuff there, the better they like it.
Anyhow, good luck and let us know where you decide to play the ED card!