Shaanxi Province Art Museum is a useful counterweight to Xi'an's archaeology-heavy sightseeing. Instead of warriors, pagodas, and imperial tombs, it focuses on painting, calligraphy, and exhibitions by artists from Shaanxi and the wider northwest.
It is worth checking current exhibitions before going, since the experience depends heavily on what is on display. For travellers already near the Small Wild Goose Pagoda or southern city centre, it can make a quiet hour with a more contemporary sense of Xi'an's cultural life.