You can find a ton of info using the search function. Like put in Oregon beach in advanced search, and check "Find posts with all of the words in any order" and then check RV Parks, Campgrounds, and Attractions and you'll get hundreds of posts, many extolling the virtues of Oregon State Park CG's.
As many others will probably also post, I'd try to go up the inland route and return via the coast. That way you are driving on the ocean side of the highway and using the pullouts is a whole lot easier.
Starting in mid-May means you can hit some of the Utah parks (e.g. Zion, Bryce, Arches) before it gets too hot. By the time you get up to Yellowstone and Grand Teton, it will be early June - late enough for much of the snow to be gone but early enough that some kids won't be out of school yet.
As you head south along the coast, it gets to be more of a pain once you get near to SF and then pretty tough driving in an RV south of Ventura. Through LA and much of San Diego, it's something to skirt way around or try to do it at night?
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!)