Patient Portal. Pediatric Center of Round Rock 7700 Cat Hollow Dr. #104 Round Rock, TX 78681 (512) 733-5437. River Ridge Pediatrics 1526 Leander Rd. Georgetown, TX 78628 (512) 863-7586. Pediatric Care of Austin 1009 E 40th St, Unit 100 Austin, TX 78751 (512) 476-5439. Pediatric Center of North Austin.