There are going to be three parts to this post. The first section is on General parts of California, and the second section is on the Southern part of California. And the third is the Northern part of California.
General California
National Park Annual Pass is totally worth it. This gives great places to hike, walk, and just plain enjoy nature. You can use it almost every where you go.
If you have the time, it is well worth the drive down the coast. We saw lots of old bridges, a huge beach with many Sea Lions sun bathing, and just enjoyed the sites to see. If you do this, plan to pack a lunch as there isn't many places to eat. Places to stop are far and few in between, but watch for them as they are there. It is windy, but not cold.
Southern California
The science museum in LA is amazing! It's free to get in, but parking is $10. Plan to spend the entire day there in hopes to see it all. The kids meals are not bad ($5) and plenty for an adult to eat (which we did). It's hands on and good for all ages.
The following website was an awesome tool to find other free things to do in LA.
http://www.welikela.com/handy-list-free-museum-days-los-angeles/
We also spent a lot of time at Griffith Park. You have the Observatory that has a lot of great programs, there are hikes, the Zoo (not free), parks, and Train Museums (is free, except the train ride for small fee)
We also learned that the San Diego Zoo and Sea World during the month of October, kids are free.
Northern California
Downtown San Francisco. I am not a huge fan of driving downtown. Hyrum loves trains of any kind. So we looked up the nearest BART stop and rode it into the bay. When we got there we purchased an all day mini and trolley pass. We then hopped onto a trolley heading to Fisherman's Wharf.
First know that food is expensive at the wharf. I was surprised that the clothing was not expensive. Take a windbreaker (not a coat) unless it's under 60 degrees.
Plan ahead. The Alcatraz tour was booked out a week. This worked in our favor because Hyrum was not (surprisingly) interested in getting on a moving boat.
There is a National Park on the west side with boats to get onto...Hyrum loved those!
Because we went to the Science Museum in LA, we didn't go to the one in San Francisco (and it's expensive). But the Aquarium would be worth going to. I took my older kids there a few years ago and they loved it, but we have an aquarium back home that is less expensive, so we didn't take advantage of this one.
Pier 39 is where you will find the Sea Lions and a lot of the fun window shopping kind of things. We actually found more Sea Lions driving down HWY 1 than we did at the Pier.
We found the Ghirardelli square thinking that we would get to see how Chocolate was made, and instead found three different stores that you could buy their chocolate or buy an ice cream with lots of chocolate on it for $5 plus. Least to say, we stuck with our granola bars and moved on.
We didn't make it to China Town or any of the other parks or stops as Hyrum's energy was done by the time we had walked the Pier's. We could have definitely used another day in downtown. We also missed the Trolley Car Museum.
Yosemite is close by Northern California and make for great hikes and site seeing. Unless you do some advance planning for camping or hotel's and food, you will want to get there early, and stay late. Where to go in Yosemite depends on the time of year. I would talk to the visitor center for which waterfalls are still going.
Big Basin Redwood State Park has a couple of great hikes that aren't too bad. Again plan ahead for food as the closest restaurant is 45 min down the mountain. They have 2 main hikes. One to the top of the mountain, giving you a nice view of the Ocean and is about 7 miles round trip and the second is a 12 mile hike down the mountain to the beach. Which you would need someone to either drop you off at the top, or pick you up at the bottom. We did the top of the mountain hike in October, we were in the shade most of the time, we took our time but still hiked for about 4 hours. It was up hill most of the way there and of course, down hill most of the way down! There was many options going up and down, but by the time we got there, and got to the top, we realized that darkness was approaching, so we went the fastest way down (which was the most up hill, and the one we took), but down hill wasn't bad.
We also went to Jamestown Railtown 1897 State Historical Park. Again bring a lunch, but it was a great site to tour with free guided tours for both kids and adults. We had a train ride (that went too slow for Hyrum) and many road stops along the way for Fruit Stands and Antique Stands.
Sacramento has an "Old Town" with many shops and museums (and of course a train museum) that was fun to wander around. The Train museum does give rides but only on weekends.