There is only one yard in Rahway, called T&E Motors that allows U-Pull-It types like us. I'm there quite a bit, since its very local (I live one town over).
Pinebrook is the other yard youre thinking off, that's off 46 almost where it crosses route 46, that's a fairly large yard actually, though lately I haven't seen too many full size trucks in there...
For quick things, or onesy/twosy items, I'll go to either one of those yards, but for larger selection I make the haul about 2 hours into PA to one of Harry's U-Pull-its. I never come back empty handed, and their prices are fairly reasonable.