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Venerable Khenchen Thrangu Rinpoche has built a classic Tibetan monastery in Sarnath called Vajra Vidya Institute. When you reach Sarnath, go to the backside of the Deer Park. The area is known as Kajoohay. Ask for directions to the "Big Tibetan Temple" or "Big Mandhir".
There are other Buddhist temples and monasteries in Sarnath: Tibetan, Korean, Chinese, Japanese, Thai, Sri Lankan, Cambodian, Vietnamese etc.