From my wife, who teaches for one of the districts named:
Cherry Creek and Douglas are both good.
Jefferson County is okay. Good neighborhoods have good schools. Bad neighborhoods have teachers who spend all damn day on discipline problems.
Aurora is about the same.
Avoid Denver proper. The schools aren't great, which makes them a perfect match for everything else about that city.
I would also avoid the Adams 50 and Adams 12 (Adams County, basically the north suburbs) districts.
Boulder....your housing budget will get you an illegal flop in a detached garage in any neighborhood in Boulder that isn't overrun with college brats.
I think, if I could find housing that I could afford in Douglas County and had a commute where living down south was convenient, that would be my answer.