In the DC area, "well run public school" is an oxymoron. What geographic area are you discussing?
Ohio, Michigan, Illinois.... there are still some poorly run districts, but some are fantastic. The one I live in now does not get the highest test scores, but they offer many advanced classes (15 different AP courses plus the more rigorous IB program). All this while about 40% of the students are considered poor, more are minorities, and the property tax rate is the lowest in the area.
There are some well run public schools in the DC area (Thomas Jefferson High in Fairfax is EXCELLENT)- but DC's public schools are a mess. There are some poorly run districts around here as well, but there are many that are VERY good.