I support public schools (these are all public schools we're talking about) but it's a basic truth that some public schools are just much better than others, mostly because of the students, but also because schools with top students tend to attract experienced educators, and more involved parents tend to steer their kids to these schools, to the extent that they can. These schools also have an "exit" process where kids who are not a good fit can be sent to other schools...most public schools do not have this luxury.
I think a move from a B- to a B+/A- school (yes, these are my ratings) is pretty substantial, but yes as I stated, I don't really feel guilty about the current schooling. It's good. I just want the best we can afford.
I'd never send my kiddos to a religious school, and the few secular middle and high schools in this area run $12,000 to $20,000 per year, so that's obviously not even an option. So we're leaning towards investing in a nicer home, which will at least add to our NW, whereas private school tuition would not.
And yes, as was said, it will save us some time, but we'd still have a 20 minute distance between school and home. But for the in-between stuff, like open houses, festivals, and such, it will be easier. And driving them to school once in a while, or picking them up early, especially the younger one, will be a heck of a lot easier.
And yes $200K is our absolute cap. I will refuse to go higher. A $130K or so mortgage over 15 years is still pretty reasonable.