The TIGER data set may have what you're looking for. It's essentially government data collected during the Census. In it's technical documentation, it has special MTFCC codes for Universities as well as Schools/Academys that you could query on (WHERE MTFCC IN ('K2540', 'K2543')). See section 6-155 here:
http://www.census.gov/geo/www/tiger/tgrshp2010/TGRSHP10AF.pd...
Take this with a grain of salt, but I believe you'd want to pull the data out of the following shape files:
ftp://ftp2.census.gov/geo/tiger/TIGER2010/POINTLM/
These files are brand spanking new, and in fact not all the data has been added yet (5 states are missing). The entire dataset for 2010 will probably be up by the end of the month.
You can see the layout of the shape file here (see Landmark (Point) Shape File Layout in section 6-104):
http://www.census.gov/geo/www/tiger/tgrshp2010/TGRSHP10AA.pd...
For what it's worth, it looks like the TIGER dataset also has school district info, which could allow you to lookup a person's school(s) based on their address (reverse geolocate their address and use the coordinates to query districts where the point exists).
If that doesn't work out (or it's missing some data) you could try looking at these websites:
http://gos2.geodata.gov/wps/portal/gos
http://www.data.gov/catalog/geodata
http://nationalatlas.gov/
http://simplegeo.com/
http://market.weogeo.com/
http://data.geocomm.com/
http://geocommons.com/
