Here are 2 plant pics I took on Fire Island nearby, which is a barrier island. The substrate is pretty much just sand. The first two pics are of the same plant.
First two pics are Sea Pea Lathyrus japonicus. Despite the species name, it is native in the area - it has a very widespread range, thanks to its marine dispersal strategy: http://linnaeus.nrm.se/flora/di/faba/lathy/lathjapv.jpg