I love camping along the North Coast--it's just beautiful!
You didn't mention North of Eureka, but Patrick's Point (about 25 miles from Eureka) is an excellent park.
South of Eureka, Richardson's Grove SP is one of my favorite campgrounds in the Redwoods. It's a state park and 'car camping' where you pull your car in and pitch your tent there, but it's not all concrete and built up. It's very beautiful and I have actually camped here alone (about 10 years ago, in my mid 20's). You can let the rangers know you are traveling alone wth the kids
Depending on when you travel, the Benbow River pools up and makes a great swimming hole. There is a big regee festival there in the summer (I think--maybe early fall) and it's a time you'd want to avoid--esp with kids, lol. Also, the Benbow Inn is very close and you can go have a nice meal if you feel the need. A little north is Garberville and you can find some places to eat here as well.
4-ish hours from Richardson's grove will put you in the SF bay area and there isn't much camping where I'd want to take my kids along the 101 corridor until you are way south, in Pismo. If you are willing to cut over to Hwy 1 you have some great options north of SF.
MacKerricher SP, another one of my favorites, so I have to mention it to you. It's near Fort Bragg. I have done an itinerary of MacKerricher and Patrick's Point and found it fantastic!
Salt Point SP, and that is another great place to camp, it's off hwy 1, North of San Francisco--pretty and on the coast. Lots to do here.
SF bay area to Pismo takes us about 5 hours (DH says less) with kids and required stops. In contrast, we can go from our home here in the east bay to DL in 5 1/2 hours (including stops) on I5. Depending on how much time you have you may want to do 101/1 and camping only to the bay area, then cut over to 5.
Let me know if you'd like more info