Last time we talked about the Southern Railroad in Griffith park. If your kids like chu-chus, it's a nice place to go. However, if they are really addicted to trains, and you want to take them to the world of trains, you should visit the Travel Town. It is located at 5200 Zoo Drive and is open from 10am to 4pm (Saturdays and Sundays to 5pm). It is an outdoor museum with a lot of real trains, and your kids can walk around, go inside some trains, and spend a really great time there.
In the Travel Town you can do a lot more than just see trains. Picnic tables and BBQ facilities are available for rental, and a lot of families spend the whole day there. You can even organize your kids' birthday or other parties there, which I haven't tried but you can find out about it calling them at (323) 662-5874. There is a nice gift shop, but you better avoid it if you don't want to spend a lot of money. And of course, there is a miniature train to ride (about 3$), which is fun and enjoyable, just like the Southern Railroad trains.