Head up the 101 about 20-30 minutes to El Capitan State Beach, Refugio SB, and/or Gaviota SB, and let the kids run around on the sand, find some tidepools, etc.
One thing if you do go to the beaches in and around SB: Watch out for tar -- it's a naturally occurring thing -- but it can be a PITA to get off skin, esp. the undersides of feet. Baby oil & baby oil wipes seem to work well.
Wine country is about 45 minutes away. Might not be a ton of fun for the kids, though. On the way, you can stop at Nojoqui Falls right off the 101 and do a short hike. I won't be surprised if there's no water in the falls, though -- or maybe only a trickle. The drought is real.
How old are the kids? If they're young enough, they might enjoy the Sea Center on the wharf. Or the zoo. (Never been, but I hear it's pretty good for a small city.)
There are whale watching tours that go out of the SB harbor. Not sure if this is prime whale-watching season, though. Maybe for humpbacks. At the very least, you'll be out on the water on a nice day. Take plenty of Dramamine, ginger pills, etc. if you're a landlubber like me.