When you arrive at Lhasa Airport or the train station, your local Tibetan guide and driver will welcome you with a Khatak (a white scarf used by Tibetans traditionally for greetings). Then he will take you straight to your hotel and advice you about the precautions from high altitude sickness, like “don’t take bath”, “drink as much water”, “take a good rest” and he go on with a list. Arriving at the hotel, he might repeat the instruction again, and you should take them very seriously.
Following morning, your guide will take you around due your itinerary, Potala palace, Jokhang Temple or one of the big monasteries and another one afternoon, but there are more to Lhasa than these popular sites, and even more to the sites than the temples and monasteries. So, if you are acclimatized with the altitude when you are still on Lhasa, take out a few hours to see the real Lhasa where the locals spend their time. Ask your guide to take you around, if not, go around by yourself with a map, most of the hotels have the government issued Lhasa and Tibet maps (for free), the maps are very accurate and clear about everything you want to see in Lhasa.
If you are not sure where to go, start from Barkhor Street, the circuit around Jokhang temple, the temple may give you an idea about the history and culture, but the street around is the live proof of what that idea means, the real and raw Tibetan lives. You will witness even more, if you take one of the streets leading anywhere into the old town, there more than a few sites to see, and a lot more to just enjoy watch and to photograph.
Then, talking about Potala Palace, there is a path around the palace the pilgrims take to circumambulate that leads to the Lukhang, pond west of the palace and the Lukhang Temple. Tibetans feed the fishes and the seagulls with breads, moving ahead the path, is a smaller square where they dance (Gorshe) in round in the summer evenings.
But that’s not the end of it, there more to explore Tibet experience about the city. Explore Tibet has Lhasa city in almost all the itineraries, but you’d like, you can customize your own itinerary with more days in Lhasa. 4 Days Lhasa Highlight