I never fully appreciated Shoreline Park until I had little kids. They have a mostly-enclosed playground with lots of sand, a few swings, and climbing equipment with slides. I felt very safe there with my 18-month old and 2.5 year old. You can watch the dogs running on the huge grass area outside the playground (which my kids loved!), or run there yourself. There is also a sidewalk that runs the length of the park, which is situated on the cliffs above the ocean--perfect for strollers or letting the kids run. Enjoy!
Great park with wonderful views, right above the beach, swings, play structure (great for ages 0-7 or so), picnic tables, BBQs. Nice walk, bike riding, lots of grass for soccer and frisbee. Tide pooling down lots of stairs. By the harbor and SB City College.