A couple of years ago, (so my memories are sketchy, please be kind) I traveled around Tibet during summer for about 2 weeks. Although there is an overland train, nasty foreigners are not allowed to use it, foreigners must apply for a permit to visit, any chinese travel agency can do this.... = $$. And we have to fly directly into the capital Lhasa.
I flew from Chengdu. Since Lhasa is about 4,500 metres, altitude sickness is a problem for many visitors, little KW was with me, and he did get sick almost immediately. - so I would not recommend this for families.
The airport is about 90kms away so there is a mad scramble for buses or rip off taxis.
Plenty of accomodation in Lhasa, here's a couple of pics of the central (old) town. The new parts of town are spawling chinese modern day shops and buildings.
Did I mention it was cold?