There are lots of well known, well respected schools on the list including Illinois, Georgia Tech and MIT.
One of them is actually where my son goes for ME.
I can only really speak for Cal Poly because that’s where he goes. They aren’t any more “project based” than any other school in that they have a senior capstone that is required and that’s it. Where they differ a bit is that nearly every class also has a lab. There are over 80 laboratories in the engineering department alone, hence part of where the “Learn by Doing” comes from. The other area is in their support for clubs. Here’s a link to the AE clubs: https://aero.calpoly.edu/clubs/. CubeSat (http://polysat.calpoly.edu/) is the one I personally think is cool. Many schools have it, but it was started at Cal Poly (wiki here: https://en.wikipedia.org/wiki/CubeSat) and the Poly Picosat Orbital Deployer (P-POD) is still to this day the primary deployment (shooting, if you will) device. I also like the fact that class sizes are generally small and the attention is almost exclusively on undergrads since they don’t offer PhD.
Look at the list and things will start to narrow down for you. Good luck.
Watch me search the entire country for a good one and than decide to go for a different branch of engineering or end up being no type of engineer at all.
I’m a female engineering student (and I’m going to respond to your comment in the ask a current engineering student thread) at Georgia Tech and we’re ranked #2 for AE and #3 for ME according to US News, I believe. Obviously we’re in the south, but I think you’ll find a pretty liberal environment at any engineering school. Certainly, that is the case at Georgia Tech. I don’t know your financial situation well enough to judge whether you should come here, but we are ranked very highly for return on investment (I think we’re #1? Not positive.). Our women in engineering program is huge, we’ve graduated more female engineers in the past 10 years than anywhere else. You can learn more at http://wie.gatech.edu/home. All of our sororities are also very highly engineering-focused and we have one engineering-specific sorority. Georgia Tech also has numerous mentorship programs, some of which are women-specific. We also allow pretty much free changing of major, and the AE/ME programs are similar enough that you can start in one and switch to the other without having taken irrelevant classes. We also have an AE minor. I hope this helps!