This site (the San Francisco Folk Music Club calendar) will give you a starting place. I believe the Sunday session in the Starry Plough (Berkeley) is not exclusively Irish, but others will see this who will know better than me I'm sure.

Depending on your interests, you may also be interested in the chantey-singing session at the Hyde Street Pier, San Francisco's National Maritime Historic Park, which Mudcatter Chanteyranger runs on the first Saturday night of every month. It's a free programme, but you must let them know you are coming. A PM to Chanteyrtanger or a telephone call to the park should cover that.

Best of luck finding something that matches your musical interests!