Hilton Head Island: Palmetto Bay Rd – Store # 00700 April 1, 2009 By Michelle. Leave a Comment Subscribe to my FREE Newsletter and get great Publix deals delivered to right to your inbox. Thanks for visiting! Island Crossing (Store #00700) 11 Palmetto Bay Rd Hilton Head Island, SC 29928-3293 Main: (843) 842-2632 Fax: (843) 842-3652 Competitors Accepted: Target and Food Lion. Thanks Billie Kay!