Either the school districts’ own websites or the state department of education should have statistics on achievement test scores, No Child Left Behind, demographic data (students in free lunch programs is an indicator of poverty) and a lot of other general indicators of the district’s health. Some districts even break it down to the school level.
Having said that, I’ve had three kids in public school and a wife who was a teacher for 30+ years and I can tell you statistics are basically a crapshoot. One extremely good or bad school (sometimes even one classroom) can skew the results for an entire district. Schools have also devised a number of ways to make themselves look good on standard achievement tests. A lot of parental involvement can make a bad school look better, while lack of parental involvement can make a good school look worse.
Some things you can look at:
How broad are the high schools and middle schools choice of electives? More electives means the district has money to spend on them, and that usually trickles down to the elementary schools, as well. In the elementary schools, look at the music and arts programs.
How are the special programs for the students at both ends of the academic scale? Schools with a good program for gifted students will work better for your kids if they’re at the top end. Schools that consider special education programs as something more than just madated warehousing programs will be a better choice if your kids have handicaps or learning disorders.
What are the districts’ net worth and tax rates? What are their records for tax votes?
What’s the physical condition of buildings? Do they have enough money for maintenance? Are the books and classroom materials relatively new?
Look at the teacher/student ratio and the staff/student ratio. If the teacher/student ratio seems high and the staff/student ratio seems low it could be because they have a lot of support staff, or because the district is padding its payroll. It’s not hard to figure out which one the district is actually doing.
A final idea: ask real estate agents in the area. They tend to know in general which neighborhoods (and which schools) make the population happy, and which don’t.
Again, looks can be deceiving. With any luck you’ll see a broad pattern that leads you to an informed choice.