Mark:
If you are interested in dropping down to a private club and getting here early, I could probably find you a spot on a Saturday with my regular group, or a Sunday afternoon at Springdale G C in Princeton. Springdale is a charming, old golf course founded in 1895 and re-designed in 1926 by William Flynn whose best courses are Shinnecock, Cherry Hills, the Cascades course at Homestead, Kittansett, Lancaster etc. etc. We still have 17 original Flynn greens and Princeton is one of the nicest suburban towns in the tri state area with Princeton University, the Institute for Advance Study, Princeton Theological Seminary, Morven the Governors mansion, etc, etc, and quite an international population.
The course itself has British feel to it with half the course bordered by the University and Seminary Buildings including Cleveland Tower -(P U Graduate College) hovering over the course and providing the symbol of the club. See GCAer Joe Bausch's pictures:
http://www.myphillygolf.com/uploads/bausch/Springdale/index.htmlPM me if interested. You can also take the train here from NYC.
You should consider driving 2 hours to Atlantic City Country Club - the best public course in the state and in a great setting. Makefield Highlands in Pennsylvania near Princeton another good bet. Royce Brook is a solid parkland track.
On a rogue note, MOST private clubs are looking for members, and if you happen to be moving to the area, and looking to join a club you could probably play many private clubs on a trial basis after meeting the Membership Chair or Manager (Wink wink, nudge, nudge, say no more, say no more).