Burqin County Museum is a small local stop, useful for grounding the region's mix of Kazakh, Tuvan, Mongol, and Han histories before heading into the mountains. Exhibits tend to be modest, but the regional context is worth having.
Visit if you have spare time in town or bad weather on the road. It will not compete with Kanas scenery, but it helps explain why this corner of Xinjiang feels so different.