Yes, you can visit the Dalai Lama's residence, called Tsuglagkhang Complex, in McLeod Ganj, Dharamshala. It is the official residence of His Holiness the Dalai Lama and one of the most important places of worship, attracting devotees from all over the world. The complex houses the Namgyal Monastery and several other shrines, temples and statues. However, the Dalai Lama's personal living quarters are not open to the public.