I'd suggest you look in a Washignton or Oregon Atlas & Gazetteer. In it, there is a list of rockhounding areas open to the public.
I'd also suggest you check with the Washington State Mineral Council, they have some really good sites too.
Here's some of my favorties though;
The Lyre River, on the Straight of J.D.F. is a great choice. In the river and down onto the beach, are agate, jasper, and petrified wood. While you are there, it is a top notch sea-run cutt fishery, and not a bad place to "surf" fish.
Gold Mountain, outside of Darrington, the Mineral Council has a collection site where you can find honey colored travertine.
And all of the creeks and rivers in the area are good places to pan for gold.
The Ginko Petrified Forest, in Vantage. The interpretive center is a great place to start a rockhounding trip, and a destination all by itself.
A good place to find petrified wood, quartz, and amethyst. It can get very windy and/or very hot here, so timing is everything.
Icicle Creek, Leavenworth. At the Johnny Creek Campground, right next to the road, is a sandstone wall, embedded with garnets, some up to the size of a pea. The loose dirt in the ditch itself, is worth panning down, garnets will hang up in a pan pretty well.
And the creek itself (Icicle) is a great place to pan for gold.
Red Top Mountain, in the Teanaway. A trail leads you up to the Red Top Lookout, worth the trip in itself, and on to one of the best public digs anywhere. Specimens include, quartz crystals, agate, and thunder egg geodes.
Ingalls Creek, Blewett Pass, one of this State's most celebrated gold rushes.
There's over 18 miles of river (much of it inside the Wilderness and "unclaimed") , it's a great place for panning, or even for exploring.
There are several stories of "lost mines" and even a story of a group of prospectors who stashed fifteen pounds of gold nuggets, when they camped for the night, only to be killed by indians. Nobody ever found that gold. A little historical research could give the grandkids a sense of "purpose", and a reason to explore.
Third Beach, La Push, a great beach and hike, has agates and jasper, and some of the best skippin' rocks on the planet.
There is another site, for thunder eggs, I want to say near the John Day Fossil Beds, in Oregon. It is supposed to be one of the best places to find geodes bigger than your head! (I tried to google up some more specific info, but I'm having trouble with my ISP).
I know it is north of the town of Madras, and south of The Dalles, somewhere around Antelope, if that's any help.
I first saw a story on the place, on the Oregon Field Guide show on PBS. Contacting them might be a way to narrow it down?
If I think of any other places I'll post again.