After a few days to sightsee and acclimatize, head straight from Lhasa to the coiling scorpion-lake of Yamdroktso before heading over the glacier-draped Karola pass to Gyantse. The town is well worth a full day; the Gyantse Kumbum Chorten at Pelkor Chöde Monastery, literally means 100,000 images, is a must-see and there are several adventurous excursions in nearby area. A 90mins drive away is Shigatse, with its impressive Tashihunpo Monastery. Shalu Monastery is a worthwhile half-day trip from Shigatse, especially if you have an interest in Tibet art.
A popular side trip en route to Mt Everest is to recently renovated Sakya, a small monastery town located just 25km off the Friendship Hey.
Finally to reach at the star attraction, Rongbuk Monastery and Everest Base Camp. Mt Everest, viewed here in Tibet, unobscured by other mountains, it's hard not to feel awed by one of nature's boldest achievements.