There are a few campsites near Pangong Lake. Some of them are available to book online. Find some here :
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You can try looking for a homestay in Maan village which is 10 km further from the Pangong Check Point. Do this at your own risk, no guarantee that the villagers will let you stay or not (there is just one campsite there called Pangong Sarai, but it is not budget accommodation). As for budget hotel goes- there are no hotels around Pangong Tso as settlement for outsiders is prohibited. You can stay in a tent at Spangmik which is the first campsite next to the lake. Tents will cost you around 1200-1500 per night.