First stop: Before you get to Big Basin, a favorite stop of ours is the covered bridge of Felton. It is also a great stop to pickup food for the picnic and have a picnic. As you can see from the map below, there is a playground (a really nice one), there is a shopping center (with Safeway) and then there is the bridge.
The bridge is really pretty and after you cross to the other end, turn left and there are stables with horses. My kids love, love watching them for a long time.
Second stop: Continue to Big Basin where for little kids and strollers the best walk is the Redwood Loop Trail
The link to the official site is: http://www.bigbasin.org/index.html
Please note that there is a parking fee: $6.00 per vehicle. There is really no other good, close place to park, so support the park and pay the fee!
There is a Naturalist Guided Walk, that the bigger kids normally like. Here are the details from the website:
March through November: Saturdays and Sundays 11:00 AM and 2:00 PM
"On this easy, level, half-mile walk you will learn astonishing facts about the ancient redwood environment and see the tallest, most rare, and most fascinating trees in Big Basin. Park docent-interpretive naturalists engages young and old alike with colorful park history, redwood reproduction, and animal stories as you explore the mysteries of the forest. Meet the Mother of the Forest, the Father of the Forest, the Santa Clara, Animal and Chimney Trees, and more. Don't miss this informative walk on this historic trail! Rain Cancels. 1 hour. Stroller and wheelchair accessible. FREE (after paying Day Use Fee)"
Third Stop: After Big Basin we normally take Highway 9 all the way to San Jose - it's scenic and a different way then always sticking to 17. On the way make sure to stop at the Villa Montalvo (http://www.villamontalvo.org/). There is a nice park at the villa and the building itself is worth a look, too. Great place for a picnic!