Yes, Long Island has a native cactus! The Prickly Pear Cactus is a mounding, low-growing perennial found closer to the shoreline in sandy patches.  Easy to grow, hard to kill, and great for containers, too.  Be careful of the tiny hairlike spines when handling!  The paddles (nopales) and fruit (tuna) are edible and feature in Mexican cuisine. 

Inhabits sand dunes, sandy road shoulders, dry fields, disturbed sites and wet meadows, with neutral soil pH. Tolerates urban pollution. The leaves change from light-green to dark-green to purple throughout the year. Grows in an attractive clump. Provides seed, nesting, and shelter for ground nesters and birds of prey.