Big Basin. For one, Muir Woods always seems crowded, parking is rough. Big Basin has some cool little waterfalls and isn't nearly as crowded.

I'm not sure where you're coming from, but Santa Cruz is a fun spot. The Beach Boardwalk is somewhat grungy, but your kids would be able to do ride a few carnival rides and the pier is cool. Our favorite spot in Santa Cruz was actually Natural Bridges State Park, on the west side. If coming from San Francisco, it is easily doable in a day. If you're staying in San Francisco, make sure to head back north on Highway 1, with a stop at Pigeon Point lighthouse and some of the fun little beaches and coves along the way. Near Big Basin, Castle Rock State Park has some great rock formations that are fun to climb on.

If you head to Muir Woods, I recommend spending time at the Marin Headlands, maybe our very favorite spot in the Bay Area: hike down to Kirby Cove, explore the battery tunnels on Hawk Hill, hike out to Point Bonita Lighthouse, do a quick visit to the Marine Mammal recovery center, and play on the black sand at Rodeo Beach. Marin Headlands provides some of the most scenic vistas in all of America.