Thomas B Norton Library Share: Public Library Thomas B Norton Library Visit Website 221 West 19th Avenue Gulf Shores, AL 36542 (251) 968-1176 Facebook Twitter Hours: Mon-Tues 10am-8pm. Wed-Fri 10am -6pm. Sat 10am - 3pm. Closed on Sunday. About Map About Free library cards to all full-time residents, adults and chlidren of Baldwin County with proper ID. What's Nearby? Distance: 5 10 15 20 25 50 mi.