Palmetto Pediatrics. 3425 university Parkway, suite 103. Sarasota, FL 34243. 941-355-1777. 218 9th street Dr West. Palmetto, FL 34221. 941-721-3900. Palmetto. Manasota. THE PRACTICE. ... Patient Portal > Where To Find Us > General Pediatrics Care. Prevention & Wellness. Immunizations. School and Sports Physicals. Behavioral and ADHD care..