In my humble (less than a year resident), Tilden Park is by far the cheapest, coolest thing for toddlers in the entire Bay Area.
Maybe it's just because we had such an AWESOME day yesterday, but we all absolutely loved the activities in Tilden Park. It's nestled in the hills between Berkeley and Orinda (so it's part of the northish East Bay).
If you are coming to the Bay Area for a vacation, or live in the area but haven't checked it out...do so ASAP!!
We headed out kind of late and arrived around 11:30. We left near 2:30 pm and held off a car-nap, so G's normal 1:30 nap was pushed to 4 pm. That part wasn't super fun or easy, but it was definitely worth it.
The park has plenty of picnic areas, hiking trails, a lake for swimming, a golf course, a little farm (small petting/feeding zoo like area), a 101 year old Merry-Go-Round, a small train with a decently long ride (plus a miniature steam train that offers ride sometimes), and great views of the bay. Check out the link above for specific details. I give this a 5 out of 5 stars on the fun and nearly free scale. We spent $12 the whole day.