The Yerba Buena Center for the Arts is an arts complex in SOMA. They have many art shows!
It was built in the late 70s. The area that the building is on was originally slated to be other things though! However those original plans (which were driven by the business community and the SF Redevelopment Agency) which entailed redeveloping a large part of SOMA in the area around the Center, including plans for a sports thing, parking lots, etc., were changed after a large tenants' lawsuit. You can get a good intro on this on Wikipedia. If you want to dive deep, the 1974 book Yerba Buena: Land Grab and Community Resistance in San Francisco by Chester Hartman is awesome (you can find this book at the Prelinger Library in SF).
In 2009 they were giving out free lifetime membership to people who got (free) YBCA tattoos at their events.
The staff who help artists set up and who do the work of installing and taking down the exhibits are extremely friendly and accomodating! So in case you are ever an exhibiting artist at YBCA, the folks who will help you install and create your work are wonderful!