In order to avoid the high altitude sickness, I took the Sky Train from Beijing to Lhasa. It takes 48 hours, but it will help you acclimatize before arriving in the capital of Tibet. Also, the views along the way are stunning so it is worth the long ride!

Lhasa is great, but the true beauty of Tibet is in its countryside so make sure you take a few days to explore the Tibetan plateau.

Here it is the itinerary I followed:

Day 1: Arrival in Beijing (If you have not visited Beijing, stay three days to explore the city)
Day 2: Sky Train
Day 3: Sky Train
Day 4: Lhasa (Potala Palace, Jokhang Temple, and Barkor Square)
Day 5: Lhasa (Drepung, Sera Monastery and Norbulingka Palace)
Day 6: Day trip from Lhasa to Nam-tso Lake
Day 7: Gyangtse (Visit Yamdrok Lake on the way, and Kumbum Monastery)
Day 8: Shitgatse (Visit Shalu Gompa on the way, and Tashi Lumpo Monastery)
Day 9: Rombuk (Visit the Rombuk Monastery and Everest Base Camp. Stay at a Tibetan guesthouse at the village nearby, or stay at the Monastery with views of the Base Camp)
Day 10: Zagmu (via Tingri, a small town with the Himalayas as a background. The road from Tingri to Zagmu, the border with Nepal, is stunning with a diverse landscape that goes from snowy peaks to forest)
Day 11: Zangmu to Kathmandu, Nepal. Cross the border through the Friendship Bridge and take a bus to Nepalese capital