When is the best time to visit?
The best times to visit Tibet are April-June and September-October when the weather isn't too cold or rainy and there are great mountain views. Late June through September tend to be cloudy and rainy. November is chilly, but still good to visit most of Tibet, as it is just after the main tourist season has ended. If you don't mind the cold, January and February have great visibility of Everest, but in March there are typically closures throughout the country for Tibetan New Year.

Where should you go?
In Lhasa, you'll want to visit Patola Palace, see monks debating at Sera and Drepung Monasteries, check out Jokhang Temple off Barkhor Square, and tour Norbulingka, the summer palace of the Dalai Lama. Just an hour away is Ganden Monastery, also worth a visit. Beyond Lhasa, make time for Yarlung Valley (the "Valley of the Tombs"), holy Nam Tso Lake, and Mt. Kailash, which is especially worthwhile at Saga Dawa time (usually May or June) where you can join pilgrims from all over the world at the most important Buddhist festival in Tibet. Other places of interest include Shigatse, Gyantse, Rongbuk Monastery, and Everest Base Camp.

How many days do you need?
With less than a week, stick to Lhasa—you can visit the monasteries and Patola Palace, with an overnight in Gyantse, in about five days. Double that, and you have time for a comprehensive overland tour from Lhasa to Nepal with stops in Shigatse, Shegar, and Rongbuk Monastery. With two weeks, combine a trek around Mt. Kailash with a road trip from Kathmandu to Lake Manasarovar. Have more time to spend? Adventurous travelers can add the Ganden Samye Trek (12 days) or Kong Tso Trek (9 days) to a traditional sightseeing trip, or spend 20 incredible days trekking the Kharta Valley.