One of my favorite little airports in NJ is Aeroflex Andover. (Here's the airnav page.) Anyone who has trained in northern Jersey probably has gone there at least once for some real short field experience.
Listed as an example of a challenging runway by Plane and Pilot magazine in their November 2010 issue, this airport presents a number of interesting features. The sole runway 2-21 is less than 2000 feet long and is just 50 feet wide. The runway features lakes at both ends, so the view on short final is a bit carrier like. With the gentle rolling hills, and dense woods surrounding the airport to the east and west, the winds are a bit shifty. Better bring your A-game short field technique. Also, a lot of antique (read no radio) aircraft are based here, so not every one is on frequency, so you need to keep a sharp eye out for traffic.
They do have restrictions on transient takeoffs and landings (I think 2, if I remember correctly), but if you want real short field experience this is the place to go. Since there are just a few dozen feet between the runway end and the water in both directions, make sure not to land long or float. (And if you are wondering, yes, flying in ground effect works pretty much the same over water as it does over land---a point my CFI demonstrated to me on one visit.)
Aeroflex-Andover is nestled in the middle of the rolling hills in northwestern NJ. So the surrounding country is beautiful from the air, especially during the fall foliage season. The people on this good old fashioned field are friendly and helpful. This is a great airport to visit in the early fall with a picnic lunch, to watch the tailwheels takeoff and land. The field is surrounded by state parks with miles of trails for some brisk hiking before heading home.
All around great little airport.
(Oh, and if you ever want to get a tailwheel endorsement, I am told this is the place to go.)