R.R.
A children's museum is geared towards little one's so he should find that fun like mine (27 months.) Bank of America and Target also sponsor free admission to museums about once a month, check their sites for dates and museums.
Are there any water fountains at parks near you? Here in North Orange County there's several and it's a great way to stay cool and have fun for free.
The OC Fair is going on right now, we went last year and he had a blast, he loved the pig races, lol! Admission on Wednesdays is free with a donation, check their site to see what they're accepting on each Wednesday. I recall that for one of them they're accepting a school supply worth $3+ and you get in free, and your son may be free anyway.
Regal theaters are offering G (and PG) movies for $1 on Tuesday and Wednesday mornings at 10 am. There's lots of theaters around us, probably the same in L.A.
One last thought is storytime at your local library. Ours does it on Wednesday mornings and afternoons. We take a sack lunch and eat outside and he gets to run around and play on the grass.
Hope this helps : )