Doug -
Have far are you willing to travel? Would you rent a car?
Hominy Hill in Colts Neck, NJ is less than 40 miles from EWR. It is a circa 1960's RT Jones course that has hosted both the Men's & Women's Publinx.
http://hominyhill.com/
DT
P.S. I have not played there in 20 years.
David's choice is a good one - solid RTJ course that was originally a private club. Conditioning usually decent, but I have not been there is many years either.
Best choice that is about 45 minutes is the Somerset County public - Neshanic Valley in Neshanic Station just west of Somerville, and most accessed via good roads from the Airport ( #78 to #287 to NJ 202). A Hurdzan and Fry design it hosted the 2012 USGA womens Publinx. Traffic going back at rush hour may be tricky, but I think you are mostly going the opposite direction.
USGA museum in Liberty Corner is about 8 minutes off the route you would take and could be a nice golf theme day.
Royce Brook is another alternative a little further away. Rutgers U course in Piscataway is decent alternative and you could take train to New Brunswick from the Airport and Uber the 9 minutes to course (3.2 Miles), then you would not have to rent a car. This is very doable by the way, trains are at least twice an hour on NJ Transit. You could get to Royce Brook from New Brunswick by Uber in about 20 minutes, another alternative. Semi local Train from airport to New Brunswick is 32 minutes. Airtran Monorail stops at all terminals and takes you to the Airport train station in about 10+ minutes. Really easy, I do it all the time.
Forsgate is right on NJ Turnpike and easy to get to. I suspect they would be receptive to a call from a Pro, and you could make it in under 40 minutes with no traffic. Play the Banks NOT the Palmer.
What day are you going?
Remember - New Jersey - Look before you laugh!
Wm Flynnfan