Titular city in The Doom That Came To Sarnath, located in Mnar. Although not directly connected to The Carcosa Mythos, the events surrounding Sarnath and Ib vaguely parallel those involving Carcosa (including the possible location of events in Arabia and location of both cities beside a lake).
A real place called Sarnath existed in India, a major Buddhist pilgrimage site (it was sacked in the 12th century and only rediscovered by British archaeologists in the 19th century). It is located close to major Hindu and Jain pilgrimage sites. Lovecraft appears to have been unaware of it.