Washington is fabulous in the summer. Summer typically runs from July 12th through mid to end of September.
I had no idea there was a scenic train ride around Mt. Rainier. I would recommend driving up to the lodge and hiking around, though. It's beautiful.
Riding the ferries is a must. You would need to ride a car ferry when you visit the San Juan Islands for whale watching (summer months is when the whales are around), or you could catch a ferry to Bainbridge Island from downtown Seattle. Or you could take the ferry to Whidbey Island, drive up the island and over Deception Pass to get back to the "mainland." Deception Pass is pretty cool. If going to the San Juan Islands, you could pop up to Anacortes and catch the ferry.
Something on the Olympic Peninsula coast would be fun. (Forks or Claloch maybe?)
I love Seattle. We have a great zoo, aquarium, downtown area for history, children's museum, the Space Needle, etc. The Chittenden Locks (recommended in another post) are a couple of blocks away from my house and pretty cool. They have salmon ladders and a salmon-viewing room.) But Tad...Amuse also had great suggestions for Tacoma.
I'm not as familiar with the eastern part of the state. I love the Cle Elum area, though.
Mt. Vernon is okay. But I bet you could find some farms/ranches up that way that you could visit that would be even more fun. Look up skagit county farms and see if any allow visitors. Find some u-pick berry farm up that way.
If you're from Vegas, I'd also suggest a "public transportation day" in Seattle. Some combination of the bus, streetcar, lightrail, or monorail would be extra fun for a 6 and 7 year old. (If you pass through Portland, it's even better down there.) I know Vegas has a monorail, but it's difficult to knit together various modes of public transit in that city.
Get ready to keep saying to yourself "It's so green up here..."