First, if you have any flexibility at all in your vacation plans as you get closer, I would pick mid-June first and mid-July second. Late June and early July are some of the busiest camping days as people try to stretch their vacations by including the 4th of July so try to avoid the week before and after the 4th if at all possible.
The good news is that at both Mt. Rainier and Crater Lake there are first-come, first served campsites in the CG's. But you'd need to get to those CG's by mid-week and plan to leave on Sunday.
Down at the beach, check some of the Siuslaw NFS CG's (Oregon Dunes). Some of those campgrounds have some of their campsites set aside for first-come, first-served. You'll have to do a little research to figure out which ones so you'll know in advance where to look. This area extends from north of Coos Bay north to just south of Yachats.
On the way up, you might consider a night at Lava Beds NM in northern CA. A first-come, first served CG only and your kids might get a kick out of exploring the lava tube caves. Take some headlamps or flashlights.
Another area to consider is around Bend, OR. At Newberry Crater NM, there are some CG's right down in the crater next to the lakes.
Brochure Fun area to explore and a lake is always something kids love to have around when you're not out sightseeing. There's a pretty cool obsidian flow right by the road in the crater. There are also NFS CG's on the Cascade Lakes scenic drive west of Bend, where there are first-come, first-served sites.
There are a couple of main areas at Mt. St. Helens, and they aren't close to each other. There isn't much camping close to the mountain, but there are a number of NFS CG's in the area.
Mt. St. Helens map Coming in from the west is the quickest access off of I-5, but camping options are limited. Seaquest SP has 11 sites that are walk up, so you might luck out there. Coming in from the east means more driving on slower state highways and NFS roads, but much more CG selection. The west side access passes by areas hit by the floods down the Toutle River and gets you up to the Johnston observatory. The east side access provides the closest road access to the crater and passes by Spirit Lake and other areas devastated by the blast.
I guess what I'm saying is that one can put together a pretty nice itinerary with some pre-planning. Know what CG's have walk up campsites and plan your travels so you arrive at a CG on a Wednesday or Thursday morning and plan to stay through Sunday.
Ken & Allison
2 Camping Cats (1 diabetic)
1996 4Runner, TRD Supercharger, Edelbrock headers
2007 Fleetwood Arcadia, Honda EU2000i
4 mountain bikes, 1 canoe, 4 tents, 8 sleeping bags, 2 backpacks
(You get the idea!)