I have done a search myself in that area (but our relocation is on hold at the moment).
Bridgewater = in the Somerset County.

This is some random information:

* Compare Schools: Great Schools GreatSchools.net
* New Jersey Department of Education: New Jersey Department of Education
* US Department of Education Parents - ED.gov

* Public School Review Public School Review - Profiles of USA Public Schools
You can: search schools by zipcode, school agency rankings by graduation / Town or county rankings
http://www.publicschoolreview.com/agency_stats.php

* Try Apartments, houses for rent, find an apartment, search rental properties - Move.com for information about individual school districts.

Maybe you would like to find out about graduation rates (high school) too, so you would know more about the specific district you want to choose: EPE Research Center - Graduation Rates Map
* 1,000 Best High Schools in America (Newsweek)
The 1,200 Top U.S. Schools - Newsweek America's Best High Schools - MSNBC.com


A ranking of the best schools per district (NJ Monthly magazine), in Somerset(= Bridgewater area):
4 Montgomery
11 Ridge (Bernards Twp)
38 Watchung Hills Regional
50 Bernards (Bernardsville)
74 Somerville
83 Bridgewater-Raritan
100 Hillsborough
163 Franklin Twp
189 North Plainfield
216 Manville
259 Bound Brook



Some other links that might be useful:
NJ.com: School report card
Somerset County, NJ Housing & School Statistics
Best Schools in New Jersey - Best Towns in NJ - New Jersey Monthly - The Best of NJ (njmonthly.com)