If you are only staying in Lhasa and cities like that, I'd go with hotels, less things to worry about. However, if you wish to see the real beauty which requires you to travel to the countryside, I know the locals are real friendly and have no problem with you staying in their house for a night or so (sometimes they ask for money though). But then you need to speak the local language as many local people don't speak English or even Mandarin.

There are a lot of hostels and hotels, but if you want some luxery than never go below 4 stars!