Lonely Planet suggests the visit to 976 Art Gallery, mentioning as one of the top destinations of Ulaanbaatar city

 

Lonely Planet:

 

This well-established contemporary art gallery features established and emerging Mongolian artists, along with a small gallery/gift shop. It’s run by Ms Gantuya, a passionate advocate for the local arts community. At the time of writing it was relocating to the Choijin Suites building in the city centre, across from the Blue Sky Tower.

 

see here