Great place to spend time!
I have been coming to the Asian Art Museum on a regular basis since moving to San Francisco four years ago. It's definitely become one of my favorite art spaces in the city. Their regular collection is strong, and has a lot of fascinating pieces to see. The space, even though appropriated from an old building, is well lit and airy, and the collection itself is curated well, and there is a good flow to the whole building.
I am a member, (which can be split with someone, so you'd share the cost and both get in free, whenever) and I find myself coming back for the revolving exhibitions, and the regular collection.
Friday seems to be the field-trip day... so if you don't like kids and art at the same time, avoid Friday mornings.