Center, TX 75935. Phone: (936) 598-3832. Fax: (936) 590-4190. Hours. Mon, Tues, Thurs, Fri: 7:30AM to 5:00PM. Wed: 7:30AM to 4:00PM. Open during the lunch-time hours for your convenience! Located in Center, Texas, Texas Quick Care is proud to serve the community's family medicine needs. We pride ourselves our putting patients first through a ....