How easy is it to find basic hotels on the day around Tibet during May?

you have to take a tour to enter tibet. the cost of rooms and transport is included in the tour. if for some reason you're able to/ want to negotiate paying for your own rooms 200rmb is fine for a basic double.

#1 - yes you do have to book through a travel agent but you do not have to take an all inclusive group tour. Travelers are free to negotiate what ever level of service you want with the travel company. The rules only force you to get your permit, guide and transport through the agency.
However agencies can often get quite reasonable accomodation rates and it always easier to have them book for you in advance - especially in high season. (but bare in mind that most travel agents in Tibet work on all inclusive type packages as this is how they make their income and many clients get agro when they discover its actually quite difficult to find good accomodation upon arriving in a little remote town!)

But - if you are traveling on a budget and like the freedom of choosing your own accomodation each night - this is totally possible if you find a flexible budget travel agent willing to do this. Finding accomodation on the friendship hwy in May should be pretty easy as it is not high season. You should be able to find accom. with attached bathroom for 200/night. But don't expect western standards of cleanliness and reliable bathroom functionality!!

We paid on average 200RMB a night for hotels and found them of fairly good quality. None were dirty and all had comfortable beds.

thanks for the replies.

I am thinking to now book the guide/transport only, and accommodation on the day.

I can only relate my experience.
The agency fee did not include lodging nor meals. I arrived in Lhasa and had the guide take me directly to my hotel of choice -- The Snowlands Hotel. I paid 250 y. It is an old place but well kept and right by Barkhor Square. I would recommend it.
On the trip to/from Everest the guide & driver would select a hotel. They would show it to me for my approval. They quickly learned of my preferences and tried to accommodate me. Only once did I turn down one of their hotel suggestions and this was no problem; they quickly found another one. But they were all inexpensive. One nice hotel cost only $2.50 U.S.!
That's it.
Happy travels!

Our driver(we didn t need a guide) took us to hotels after leaving Lhasa and we found them all to be of a good standard. Maybe he got a kickback, who knows and even if he did, it didnt impact on us.