We spent a few days in Labrang last April (2103), with our family (2 kids, 4 and 6), coming from Xi'an and on our way to Dunuhang.
A great tibetan monastery, far more impressive than the one in Shangrila due do its size but also to the activity within the monastery, with a lot of monks (~1500) studying and praying - and barely no tourists (I think we were only 10-15 all-in-all). Explore the monastery with a monk, don't miss the library (with thousands of wooden sutra) that you can visit if you manage to find a monk willing to open it for you, and try to attend a ceremony in the great hall.
We stayed 3 days - one afternoon spent in the grasslands (but we did not go far enough - might probably be worth doing it with a guide) and it is sufficint to have a good glimpse of the monastery. We contacted Clary van Meijel (Nomad Travel) who helped us to organizewa our trip from HK, from a car pick-up in Xi'an, the booking of the night train to Jiayuguan and the transfer by private car to Dunuhang + local hotels : she managed to have it customized to our need with good advice, was very flexible and proved to be very reliable - I would definitely recommend going through her agency, especially when not speaking chinese make the local organization a bit more difficult.