Lake Balboa (AKA the ‘Duck Park’) is one such possibility. It’s huge, and everyone can fish, bird watch, play with remote-controlled boats, or play in the large playground. There are plenty of large grass areas for everyone to relax in and play some ball. Families can come and go as they please, and can spend a long time here without breaking the bank. For a much larger-scale park experience, head on over to the Las Virgenes Canyon Open Space Preserve. This park features hiking trails where families can experience seeing a huge variety of native and endangered species of plants, trees, and animals. A truly magical experience.
Travel Town Museum is another great choice. Families can enjoy free admission for touring the many types of stationary trains and can even take a ride on various-sized miniature trains for a small fare. This museum is hands-on, and they have loads of trains to go through. Everyone can learn some local history and then visit the gift shop to purchase mementos of the memories created here. Some other museums worth checking out are: Discovery Cube LA, Skirball Center, and Warner Brothers Studio, which also includes a tour of their working studio.
Just a short drive north of the Valley is Kids World Family Fun Center. They have a huge indoor play structure that includes foam ball cannons, slides, zip lines, and a sectioned-off toddler-only area. They also have a basketball room, an all-ages arcade (with both video and redemption games), bumper balls, and a super cool laser tag arena. They also have a surprisingly good restaurant with an excellent variety of food. This place doesn’t charge for adults or infants, and families can stay until closing.
I recommend trying all of the places mentioned above over the span of several weekends. Then your family can decide which places they like best and occasionally return for more adventures.
You can find detailed information for each of these places, such as the address, directions, hours, and pricing on their respective web pages on the internet.