Smart, savvy folks who aren't dominated by prestige, elitism, and what the neighbors will think are good at finding the hidden gems...like a CWRU or a Rochester or Stevens or WPI, or at the LAC level a Denison, a Whitman, a Centre, a Rhodes, etc...You might give up some sunny days and 40 to 50 degrees in temperature and 15-20 ranking spots in USNWR, but the academics are just as good in most cases (and maybe sometimes better), athletic opportunities might be a bit more attractive, and you might get some very helpful merit money. Even for those of us who realize rankings shouldn't be so focal and overwhelming in our minds, it's very difficult at least for people within a particular demographic to truly break free from the false idol of rankings. We learn about and live them as though they have some hard reality...and the impact of that is huge and leads to categorizing schools in ways we basically accept as real that aren't real....like "so and so is a top 5 school" or "top 10 school" or a "that one's OK, it's still top 40 or 50." And the industry knows how powerful the mythology is because some of them are laser-focused on improving their ranking...and why not when doing so yields very clear results, more applicants, lower admissions rates, more money, better facilities, and whatever else goes along with substantial reputation boosts (see Colby, Richmond, Denison, etc). We assign different meanings to a school that's ranked #5 versus one that's #25 even though your kid's chances of as good an outcome and in many cases even better outcomes (med school, law school, careers) may be significantly better at the one ranked #25 or even #75. This stuff gets so ingrained we often don't even realize what we're doing. Someone could tell me his kid is seriously looking at Gustavus Adolphus, and my kneejerk response might be something like "Oh wow, that's nice. St Peter, MN, right? Is she considering Grinnell out that way as well?" The frames and filters we "wear" everyday are so much more dominant than we think they are.
But be careful. Your kid may actually listen and ultimately disappoint you. I loved Rochester and "discovered" it in our family. In my mind (and I suspect this is often the case with CWRU) I considered UR to be the almost perfect high-end safety school for my daughter...and good enough for my ego if that's how things played out. Nevertheless, when she had all of your choices in front of her after all the acceptances, wait lists, and rejections came in, I could not help wanting her to pick Macalester, Bryn Mawr, Barnard, or NYU. It was all ego, ego, ego. I knew UR was every bit as good as any of the others and in hindsight she and we never had any regrets (jokes about paywalls aside), but I still imagined lukewarm social responses when others would hear about her choice...like, with a slightly puzzled look "Oh, Rochester, nice school" and then watching that couple move on to the parents jabbering about Dartmouth.
Back to CWRU....I think you are correct @Kuiper that the medical excellence now synonymous with Cleveland because of Cleveland Clinic and also to some degree Case Medical has a positive contagion effect on CWRU in general. Cleveland in terms of medicine is considered absolutely on a level with Boston, San Fran, Baltimore, NYC, Rochester, MN, Toronto, etc....but all things being equal, how often is a kid who holds acceptances from U Michigan, UVA, CMU, Wash U, Emory, and CWRU gonna choose CWRU? Not often unless the money difference is extreme and a critical factor.