Your budget will limit you to 2-3 bedrooms with 1-2 baths, in my suggesting areas,
Try East Hanover, Hanover (Morristown County, most likely condo) and Union (Union County, single house).
Livingston (Essex County)is the best when considering kids' education.
The property tax is sort of high at Essex county, eps West Orange. Also avoid Jersey city, Newark, and East Orange if you can.
Morristown county is better.
Edison (Middlesex County) is famous as a Chinese community
Public transportation should be under consideration because of tunnel toll and traffic.
http://new.gsmls.com/public/selectaCounty.jsp