If you persevere and drive to the very end, to Sandy Point Reservation, park your car, grab your gear and hike along the beach for another 1/2 mile you will arrive at an area that's roped off to protect nesting Piping Plovers and Least Terns. The terns will let you know if you get too close, by dive bombing your head until you retreat. The ropes are there to protect the few nesting pairs of Piping Plovers hid in the grass.
Piping Plovers are a threatened species which is why the refuge beach is shut down. the state is a bit more relaxed just roping off a substantial area of beach. Unfortunately they didn't tell the plovers about the rope, so while the nests are protected, you can encounter the birds anywhere.
This spring's flooding wiped out their original nests. However, the plovers and terns have "re-nested" and are incubating their eggs. Here are a few photos from a recent visit.