Hamptons Jazz Fest continues with Stan Killian Quintet (Parrish Art Museum, December 16). Damien Sneed’s “Joy to the World” puts a gospel/jazz spin on holiday tunes (Westhampton Beach Performing Arts Center, December 17). Studio 3’s “Mixed Nuts” presents a family-friendly twist on “The Nutcracker” (Bay Street Theater, December 16-18). Pianist/singer Judy Carmichael performs “Let’s Swing!” (Bay Street Theater, December 17). 279 Montauk Highway, Water Mill, N.Y., 11976. 76 Main Street, Westhampton Beach, N.Y., 11978. 1 Bay Street, Sag Harbor, N.Y., 11978.