How does CMU stack up against MIT, U of M, and other Ivies? Is it considered a reach ALL of the time like most top schools? I’ve already looked at the common data set for CMU so I know how high of scores are needed( particularly in math), but is it considered a prestigious school? Any insight will be helpful. Thank you in advance.
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CMU’s Computer Science and Theater departments are as good as it gets. Otherwise, I’ve heard CMU described as the place you go if you can’t get into MIT.
CMU is my favorite school, with no close second (I haven’t visited U of M but know MIT, Yale, Brown, Berkeley, and Harvard well.). Unlike MIT, CMU’s environment is intellectually very diverse. The campus is extremely well kept. The talent the school attracts is incredible. The Department of Defense just earmarked $1.7billion to CMU, and many other areas of the government, as well as the private sector, are investing enormous amounts of money on CMU. Google and Uber (and many other tech companies) have headquarters in Pittsburgh because they want to be near CMU. I wouldn’t be surprised if within the next few years CMU surpasses its peers (including MIT) in many STEM areas. I have a good numbers of friends (not limited to friends in CS) who turned down MIT (or didn’t even apply to MIT) for CMU. If I couldn’t attend CMU and had a chance to choose, I’d pick many other schools before MIT (UWSL, University of Chicago, University of Maryland College Park, University of Michigan, and Stanford, among others). CMU was also John Nash’s (alumnus) and Randy Paush’s (professor) school. 
Pittsburgh is a great city, by the way.