Huntington Library and Gardens, Los Angeles
Address 1151 Oxford Road, San Marino, CA Map, Website
Lots of spaces to run, walk or stroll. There's admission fee for adults but in the process you can visit several art museums with very interesting american art collections. The garden has several sections: Japanese Gardens, Australian forrest, cactus garden, rose garden, tropical conservatory and an herb garden where kids can smell and taste various herbs.
You can't have picnics on the lawn but there is a tea-house with sandwiches and drinks.
It's a great place for kids to learn about flora. Summers can be hot, so bring plenty of water, so best time to go is spring and fall.
There are some steep hills, but they're all stroller accessible.