You could find out the names of the schools that would be in your new area, call them and see if they have a website you can look at. If your new area isn't too far from where you live now, arrange to take a tour of the school. Get a feel of it. Look at the children's work that's hanging in the hall. Check out the play ground. Talk to the principal. Ask to observe a class in session. Find out about arts programs, and other enrichment programs, special needs and gifted programs. There's usually information about standardized test scores, but that shouldn't be the only thing you look at.
Do you know anyone living in the area you want to move to? If so, talk to those people about the schools.