I'd skip Death Valley. Maybe head straight for Sequoia and north from there.
A fun park for kids is Lava Beds NM. Lava tubes (think caves) to explore on your own. Bring headlamps and/or flashlights. First come, first served CG that we liked.
As noted, head north inland (Lassen NP, Crater Lake, Bend, Lava Lands, Newberry Crater, Mt. St. Helens), then head south back along the coast. (In the Bend area, maybe half of the campsites in Newberry Crater are non reservable. The CG's are right on the water. It's like camping on the lake shore at Crater Lake. Part and sightsee from there for a few days.)
Can you go without reservations? I suppose yes, but in some cases you won't be staying anywhere near the more popular NP's. It's a choice between being tied down and being right there vs. retaining flexibility and having to drive two or three hours every day round trip to get into the major parks like Yosemite. But for places in between, you can often find NFS CG's if you stop early and aren't travelling on the weekend. And lesser visited parks like Lassen have quite a few first come, first served CGs. Just don't show up at 6:00 p.m. on a Friday and expect to find a site. Lassen has some interesting thermal features like Yellowstone but on a smaller scale.
The flexibility that agesilaus touts is because he stays in private CG's. Public CG"s at NP's and SP's tend to book and fill for the summer.
Similarly, the SP's along the Oregon Coast get booked up in the summer. How important is it for you to be camped within walking distance of the beach? Also, the northern part of the OR coast gets really busy on weekends with crowds from Portland.
Things get really busy on the weekends. Without reservations, you might need to find a campsite by early Thursday a.m. and stay until Sunday.
But reservations don't necessarily tie you down. Consider the Oregon Coast. Pick a SP and camp for several days. Each day you can head out in a different direction and explore what you want at your whim. Tidepools one day, lighthouses the next, Tillimook Cheese factory (and ice cream) another.
Given your desire to be flexible up to a point, I'd stronly encourage reservations at Yosemite. You have to be on line at the moment the reservation window opens to have any hope of a reservation. I'd also suggest getting a reservation or two along the Oregon Coast. Check out Tillicum Beach NFS or Beachside SP to get a spot nearly on the beach. The Oregon SP's are exceptionally fine and well worth the hassle of reservations IMHO.