When our kids were 6 and 8 we did a week-long Maine trip, camping at Peaks Kenny State Park and then at various points in Baxter. Out of ~ six nights away from home we were backpacking two (nights at Chimney Pond bracketing our Katahdin climb). That was one of the best vacations we've had.
Two summers later we flew into Seattle and spent five weeks car-camping our way down to Santa Cruz, with a few breaks at friends houses and one longer backpacking trip in Yosemite. A few of the areas where we spent time would probably fit the bill for what you're asking about. The orbit from Seattle out to Olympic National Park and back would make a great week, with good camping, hiking, beaches, rivers, and hot springs. Highlights include the Sol Duc and Hoh areas. You could also make a cool week with hiking, rivers, tree-watching, volcanic features, camping, and hot spring opportunities out of the axis between Lassen Volcanic NP and Redwood NP in northern California. Or, the circuit from the Bay Area to Tahoe to Yosemite is stuffed with more recreational opportunities than you could exploit in a lifetime.
We camped and hiked our behinds off, but more domesticated options like indoor lodging, dining, museums, etc. are available in or near all of these areas.
Are your kids pretty well accustomed to hiking and camping already? I think one of the things that made these trips work so well for us is that our kids were already pretty fluent in these activities, so we were going on the road with a skill set they were already very comfortable with.