Griffith Park is one of our favorite places to explore near Downtown Los Angeles. The Travel Town Museum is perfect for the train obsessed child. There are full-sized locomotives and passenger cars, a miniature train that everyone can ride through the park and a small museum with railway memorabilia.
There is a large free parking lot, picnic tables and a snack shack. I met another mom and her son on a weekday morning and it was very quiet. It was great fun and a perfect place to explore with little cost.