<font color=navy>I live about 20 mins or so from Downtown LA.
I recommend going to the La Brea Tarpits. It is easy to get there - you take 7th street west and it turns into Wilshire Blvd (you should still get a map to pinpoint these places & how to get there). The La Brea Tarpits is on the right hand side, and just two blocks further you'll reach Rodeo Drive (if you're interested in seeing that). The Tarpits are in a big park, and behind them is a museum where they've recreated the animals from the bones escavated from the pits - The wooly mammoth is huge. They also have sloths, saber toothed lions, etc. If you go a few blocks north of the tarpits you'll hit Farmers Market, and across the street from that is a nice mall, etc. I figure that driving there from Downtown will take you anywhere from 15 mins to a half hour.
Taking the 110 freeway south, in about 10-15 minutes, you'll reach the Coliseum (where they held the 32 & 84 Olympics), the USC campus, and two museums that the kids might like -- the Natural History Museum and the Science Museum - the Science Museum is free and has hands-on exhibits that the kids can do. There is also an IMAX theater there (& I believe the Lion King is playing there) and you can see a film. There is also a rose garden - nice for a picnic, etc.
Taking the 110 north will lead you to the 5 north and eventually to the LA Zoo. It's not far at all. You can also go to Descanso Gardens (for a fee), which is a HUGE garden in the foothills, with all kinds of plants, flowers, Japanese tea garden, koi pond, etc., where your kids can run as much as they want, and you could probably get some good pictures of them.
Close by, you can visit Olvera Street (birthplace of El Pueblo de Nuestra Senora, la Reina de
Los Angeles de Porciancula (I can see why they shortened the name
)
If you take the 110 south to the 10 west, you'll end up in Santa Monica & can go to the beach there. Give it about a half hour.
If you take the 110 south to where it ends in San Pedro, you can visit Ports O Call, and near that is the Cabrillo Beach Marine Museum, with a protected beach nearby and even a little park. If I remember correctly, they have a tidepool area where the kids can touch the sea animals. And speaking of tidepools, in that same general area, you can visit the tidepools, which is interesting at low tide.