Not only can one gain spiritual calm in Sarnath by independent meditation, but there are classes and temples galore where a novice can learn about Buddhist law through the teachings of the different sects. The Thai temple offers classes in Theravada ("the Lesser Wheel") teachings and practices, as well as yoga and mediation classes. I believe these classes are open to everyone. Recently, the Tibetan temple also offers classes, but I believe they are targeted to actual practitioners of the faith, i.e., monks. I believed there was also a Japanese temple that can give you more information on teachings of the Greater Wheel. I can't remember all the temples, there were so many that it was hard to keep track of all.
For those wanting independent meditation, the setting of Sarnath is perfectly conducive to such pursuits. Here you can meditate without being disturbed, and without being distracted by the traditional noise and hubbub that are inherently a part of Indian life. Amazing for India, the grounds of Sarnath were off-limits to cows, snack-food sellers and the whole gamut of Indian street life. The small size of Sarnath also contributed to maintaining the city's calming spirit-Sarnath was free from motorised transport, and one can easily get around the whole city by walking.
I chose a spot of ground not too far away from the Dhamekh stupa, but for the entire two hours that I sat, I felt no encroachment on my space. Other practitioners of meditation in Sarnath generally found peaceful places of their own, far enough from each other so as not to be a source of disturbance. Because the grounds are extensive and beautifully maintained, you won't have difficulties calling a spot your own, if only for a few hours. The grounds are extensive, beautifully maintained, and as befitting its reputation as a deer park, the deer are still there in Sarnath, some 150 of them. For a few hours of stillness, or for longer periods of meditation, there is no comparable place in India.