Why it's controversial: Many activists warn that traveling to Tibet puts money into the hands of the Chinese government, rather than the Tibetan people, and perpetuates both cultural genocide and the "Disney-fication" of Tibetan beliefs. The Free Tibet campaign notes that visiting also provides legitimacy to Chinese occupation. "Travel in Tibet is conducted on the terms laid down by the Chinese, not by Tibetans, and always involves some degree of compliance with policies and security measures of the Chinese regime."
Instead go to: Dharamsala, India, where you'll find the Dalai Lama's residence and the headquarters of the Tibetan government in exile. Dharamsala is also the starting point for a number of great Himalayan hikes through the Dhauladhar range.