Naval Health Clinic Cherry Point. Contact Us. Building 4389 Beaufort Road PSC Box 8023 Cherry Point, NC 28533-0023. Get Directions. Naval Health Clinic Cherry Point website. 1-252-466-0921. 7:30 a.m. - 4:00 p.m. ... We send out surveys to a sample of our patients after their health care appointments. We measure your satisfaction and study ....