Tilden Park in the Berkeley Hills is a pretty cool place for toddlers. I used to go there regularly as a child, and now that R is old enough to like it, my family couldn't wait to take her. We visited this weekend.
Attractions include a rideable mini steam train, a museum (with lots of child-friendly elements, including a magnet wall), a lake, a small model farm (which includes various heritage breeds of farm animals), playgrounds, and an antique carousel.
As a kid, the carousel was always my favorite. It's over 100 years old, and all the animals are hand-carved and hand-painted (most are really beautiful works of art). I have many happy memories of riding it, bestriding a frog or zebra or dragon as it spun around.
R had a great time (as you can see from the picture). She even picked out which animal to ride on her second trip (she chose the lion). It was really cute. I had a good time watching her of course, but also because the carousel is beautiful. Now that I'm an adult I can better appreciate its artistry and historicity (I would seriously display any of the animals in my house).
Admission is quite affordable ($10 for 7 rides), parking is free and easy, and they even sell popcorn at the attached gift shop. This is the sort of thing they do not have in Singapore, so I was happy to share it with R and relive a little bit of my childhood.