Laying his claim.
If you turn left (south) after crossing the bridge you follow a wide fire road along the San Pablo Bay. I think it's a perfect distance for 3-6 year old legs from there to a beach with a big Eucalyptus tree at its edge (I say that but know that they're removing a lot of the old Eucalyptus trees). There are views, butterflies, horse poop, acorns, rocks, and a whole lotta space to run.
Another option is to stay on the paved road which runs down the middle of the peninsula/park. It leads to some picnic areas and a rustic playground. While I'm not a fan of playgrounds in general, this is a pretty nice one. It's big and spacious and wooden with beautiful views. One of my kids discovered clay under the sand on one visit and now immediately starts digging to make yet another clay baseball.
With Mt Tam behind.
Something we haven't done yet, but want to do, is head out to the pier at the northern point of the park. There's a shuttle to take you there if your legs or wheels (the bicycle or scooter kind) can't get you there. Check the sign near the parking lot to see the schedule.
We got a wave back.
One of our favorite parts... wait... one of Ben's favorite parts of this park is the train track that runs right by it. If he had his way we would sit by the tracks or on the bridge that goes over them and watch the trains all day. He would also like the trains to come more frequently than they do. Plenty of time has been spent just sitting on the bridge waiting to hear the whistle or the rumble of the Amtrak. I recommend bringing snacks for these kinds of occasions. And lots of patience.