Neurology Healthcare Providers in Johnson City . ... tri-state mountain neurology. 1321 Sunset Drive, Suite 11 Johnson City, Tennessee 37604. Monday - Thursday 7:45 am - 4:45 pm Friday 7:45 am - 12:00 pm Saturday Closed. Sunday Closed ...PHYSICIANS‧NEW PATIENTS‧SERVICES‧HEALTH PLANS‧CLINICAL TRIALS‧CONTACT.