Tongren is pleasant from April through October. The Monlam Chenmo festival, usually in February or March according to the Tibetan calendar, is the most atmospheric time to visit — pilgrims arrive from across the region, the monasteries are at their most active, and the valley is crowded with tents and prayer flags. Summer weekends bring Chinese domestic tourists; weekdays are quieter.
Note that during late July to early September women are traditionally not permitted in certain areas of Wutun Upper Monastery. If you want full access, plan around this restriction.