Aransas County Farmers Markets Rockport Fulton Market Days 100 Seabreeze Drive Rockport, TX Rockport, TX. Days of Operation: Third Saturday and Sunday of each month. Hours of Operation: Friday 12 p.m. -5 p.m. Saturday 9 a.m. -5 p.m. Sunday 10 a.m. – 5 p.m. (361) 463-0125 Website: http://fultonmarketdays.com/about-us-1/