Starbucks closed through Aug. 15 Shared By: contributorAugust 14, 2023 Due to network issues, Starbucks will be closed through Aug. 15. The coffeehouse is working to resolve the issue. Starbucks hours at UT Health San Antonio are from 7 a.m. to 4 p.m. Monday–Friday. The phone number for Starbucks is 210-450-8078. Share This Article!