“For example, our son wants to major in computer engineering or computer science, for which our state flagship, UMass Amherst, is good.”
I think that there are two issues here. One is in general how do you trade off the cost of education versus the quality of the education and the “fit” between the student and the school. The other is what to do in the specific case of a CS major who is in-state for U.Mass Amherst.
I have worked with a very large number of software engineers who are graduates from U.Mass Amherst. I have also worked with quite a few software engineers who are graduates from MIT and Stanford. U.Mass Amherst is VERY good for CS. The top graduates that I work with from there are just as strong as the top graduates from MIT and Stanford. I could (but will not) easily name multiple really top people with really top jobs (and a few without a job because they retired rich) who graduated from there. If given the chance to study CS at the same cost at either U.Mass or Harvard, personally I would probably choose U.Mass, or choose whichever one the student felt more comfortable at. MIT or Stanford or CMU would be a harder decision. These are top schools for CS, but are also very academically demanding. If able to pay, I might pay for MIT or Stanford or CMU, but only if the student really wanted to do it. One thing that might make me more willing to pay in this case is that CS is a major where you really can be done with your education with your bachelor’s degree.
The more general question is probably more difficult. In our experience there was not much correlation between the academic reputation of the school and what it would cost us. For example, McGill is the highest ranked university that either daughter was accepted to, and was also one of the least expensive (it would have cost us less than our in-state flagship). However, this is due to factors that are specific to us. The most expensive schools that either daughter got into were Northeastern and BU. We ruled them out due to cost (we would have been full pay). However, in retrospect they would have been a bad fit for our children. Again this is due to factors that are specific to us. Right now I am paying an absurdly small amount for a school with a very strong program in my younger daughter’s major, and she is getting great opportunities such as research projects and a coop. She knows her professors and loves her school. Again however this is due to factors that are pretty much specific to her. I think that each student and each set of parents needs to find a school that fits them. There are so many factors to consider, including cost, and they are going to vary so widely from student to student.
Neither of our daughters went to the school that would have been the least expensive. Both went to schools that were relatively reasonably priced, were a good fit, and had very strong programs in what they ended up majoring in. Given that both changed their majors, this last point might have been mostly luck.
In general I think that the overall ranking of universities is given too much consideration. Individual fit and individual programs matter a lot. Avoiding debt also matters a lot.