I live right in Middlesex County right near New Brunswick. There aren't any places too close. The best ranges around are...
Ray's Sport Shop Inc.
559 Highway 22
N. Plainfield, NJ 07060
908-561-4400
Shore Shot Pistol Range
730 Airport Road
Lakewood, N. J. 08701
732-905-6888 or
1-888-357-2264
Old Bridge Rifle & Pistol Club
PO Box 586
Old Bridge, NJ 08857
732-360-1987