Living in the SE of England and spending most summers in Northern California (many of which were as a child or with my young children, I'd like to add my ha'porth.
As alluded to above, coastal Northern California is often / usually cold and foggy in August, its worst month. But 5 miles inland, it's guaranteed hot. The landscape is somewhat reminiscent of Northern Cornwall but the water is freezing cold (which is why it can be so foggy, because of the hot inland air colliding with the cold ocean air). Much of the coastline within 50-60 miles north or south of San Francisco will likely be cold and grey, and the local architecture can make things seem even more grey - none of the brightly coloured cottages which you find in seaside Cornwall.
From my perspective, Santa Cruz is tacky and grey and Elkhorn Slough was disappointing in that it did nothing to dispel notions of David Brent's habitat from my mind. Likewise, I would avoid Half Moon Bay, Bodega Bay, Stinson Beach etc for much the same reasons.
Having done the negative, I'd like to add some positives, of which there are far, far more. Monterey's Aquarium is absolutely fantastic and the children - and adults - will love it. If you can stomach the drive to Yosemite, I would stay in Carmel (the town of which Clint Eastwood was mayor). It's charming and, importantly, it's all walkable (if you stay on Ocean Avenue). The beach there is sheltered and stunning and, as long as you avoid weekends, very uncrowded. Plus there are great ways of scrambling across to Pebble Beach (underneath the famous golf course). My children enjoyed finding lost golf balls under the cliffs. It's just a short drive to Monterey and its Aquarium.
In that area, your other option is to stay in Carmel Valley, which snakes inland from Carmel and is usually outside the fog bank. There are nice resort style hotels there, but you would have to drive in to Carmel for the beach.
Reading your OP, I really think that Carmel would fit the bill for a father and child break.