Most (if not all) of those schools have a better national reputation than UM anyway.
I was accepted to Michigan twice; once for undergrad and once for graduate school. After I was accepted for undergrad, I went to tour the campus and talked with a fellow high school junior who was on the tour. She was from Michigan and UM was her dream school. She was shocked and impressed that I had already been accepted and was appalled when I told her I wasn't sure if I was coming. UM has a weird sense of self importance. It is a good school, but is not significantly better than a lot of other large public universities (UNC, UVA, PSU, etc).
To add to that, as another poster said, for STEM graduate school the most important things for where you go are not the school (I mean, it matters; you don't want to spend years of your life somewhere that you hate). The reputation of your adviser carries way more weight than the school you attend, but you also need an adviser that you can work with. (just for those on the board who maybe aren't familiar, your STEM graduate adviser isn't like your undergrad adviser; they are essentially your boss for the duration of your studies. They have tremendous ability to help you out (both in school and later in life) but they can also make your life hell).
First, make sure you have an adviser who actually wants you as a student. In other words, talk with them ahead of time and get to know them as much as you can before you decide to enroll.
Second, talk to other students (and if possible recent graduates) who have worked with that adviser. They will give you some sense of day to day life, expectations, things to be wary of, etc.
Third, and this should go without saying, you shouldn't be paying anything out of pocket for a STEM degree. If UW will give you a research assistanceship (full tuition, plus a stipend or salary), but Havard won't? Hello Huskies.