To attend your public school of choice, you need to be living within that school's service boundaries (with a few exceptions). If you're not sure what the boundaries are, check with your realtor, school or county website.
DC
DC Public Schools: http://dcps.dc.gov/portal/site/DCPS/
Maryland
Montgomery County Public Schools: http://www.montgomeryschoolsmd.org/Prince George's County Public Schools: http://www1.pgcps.org/
Virginia
Alexandria City Public Schools: http://www.acps.k12.va.us/Arlington County Public Schools: http://www.apsva.us/City of Falls Church Public Schools: http://www.fccps.k12.va.us/Fairfax County Public Schools: http://www.fcps.edu/
In DC:In Prince George's County: http://www1.pgcps.org/ib/In Fairfax County: http://www.fcps.edu/is/aap/ibdiploma.shtmlIn Falls Church City: http://www.fccps.org/gm/index.php?option=com_content&view=article&id=83&Itemid=181
Honestly, there are too many to count. Here's a fairly useful list of schools with their websites: http://en.wikipedia.org/wiki/List_of_parochial_and_private_schools_in_Washington,_D.C.
Global Community Liaison Office (GCLO)
GCLO's website has links to DC metro schools, preschools, childcare and much more.