Liquor stores in Sullivan's Island, South Carolina The most complete information about Liquor stores in Sullivan's Island, South Carolina: Addresses, phone numbers, reviews and other information. All stores Clothing Convenience Furniture Home goods Jewelry Liquor Supermarket All liquor stores in Sullivan's Island THE CO-OP Sullivan's Island Liquor Supermarket Closed now Until 07:00 am 2019 Middle Street, Sullivan's Island, SC 29482 Get Directions Contacts Write a review