A friend of mine is hosting some Japanese high school exchange students for a few weeks here in the Seattle area. And those kids must be entertained. Of course, since they are in America, they must be entertained in a stereotypical American style.
So, I’m coming up empty here. Visit a cheese factory? Go bowling? Elk hunting?
Of course I forgot the one I already had, which apparently is to visit the original Starbucks in Pike Place Market. Seriously, it’s packed with Japanese tourists all day every day. So there’s that.
Baseball game? I hear Seattle has a team of middling competence.
ETA: Assuming it’s during baseball season of course…
Shooting range. It’s something they’ll never experience in Japan.
A group of teenagers who have probably never held a gun in their life?
No way.
Not to mention possible language problems.
Unless you can rent the whole range and a bunch of instructors.
I’m just saying they’ll be heroes to all their friends back home.
Typical tourist stuff:
A ride on a Washington State ferry
Visit Ballard Locks
Space Needle
Isn’t there a Boeing plant that offers public tours? I’ve always wanted to see that, but I like factory tours. And didn’t the co-founder of Microsoft open a museum dedicated to Jimi Hendrix. (But would a teenager today even know who Jimi Hendrix is?)
American football or baseball would both be popular if you could take them to a game, or at least get some merch. Getting to visit a lot of different American homes would also be an eye-opener for them. Museum of flight is pretty cool. Is it too soon for a BBQ in the scenic outdoors?
Smoking weed and getting laid. You probably should not facilitate either one, but you asked what the kids want to do…
I have hosted Japanese students several times, both individually and in groups, and almost all of them said the most fun they had was going shooting. You could take them to a range, or just out in the boondocks for some soda can pinging. Bonus points for skeet shooting.
Also go to the Ballard Locks, Space Needle, Pike Place, Experience Music Project, Museum of Flight, etc. IOW all the fun things you would do to entertain any visitor to Seattle.
Surely that evidence suggests that this is a Japanese activity rather than an American activity? 
I wouldn’t suggest a baseball game since they can go to those back home. That’s why when I was in Dubai I rode a camel instead of going four wheeling in the desert.
It’s really not that hard to show someone how to shoot, especially if you’re using something simple like a single-shot or bolt action .22 rifle, or a Glock handgun.
Over the years I’ve shown lots of people who’ve never held a real gun before how to shoot and nearly all of them picked up the basics very quickly.
Go to a Japanese restaurant, too. That’s another thing all my students enjoyed.
Do you have any go kart race tracks? Any outdoor activities would be good. I like the shooting idea. None of the kids would have ever seen a gun so even a .22 would be exciting.
One word for you: Outlets Mall 
Do we know where these Japanese students are coming from? Big city, little towns, where? City slickers may like hiking, Snoqualamie Falls, horse back riding, skiing (lot of snow), salmon fishing, whale watching, etc.
Experience a drive in like Burger Master.
Leavenworth for pure German Americana.
I lived in Japan for 2.5 years. Not the same but French exchange students liked desolation point. We stopped at the shrimp shack with fresh shrimp and exotic food like elk. It’s cheap too.
Pike’s Place and Starbucks is mandatory. The shooting should be well liked.
Don’t go to Japan Town - the Japanese were all sent to camps in WW2 and never came back. It’s a China town now. They can go for Chinese food though. Uwajimaya supermarket for ny foods they miss or if they want to cook for the hosts.
Also, are they boys, girls or both?
McDonald’s is everywhere in Japan, so that’s nothing new, as is Domino’s. However they would probably like places that have different sorts of hamburgers and pizzas.
The last time I talked to teenaged Japanese about their experiences in American homestays was about 30 years ago, so things have really changed.
However, everyone is surprised at the volume of food. Make sure to tell the kids they don’t have to eat everything.
Don’t be surprised if they want rice after a couple of days. Stock up on some instant noodles.
How about a local concert, festival, fair, etc.? I don’t know what might be going on in your neck of the woods this time of year (and they definitely missed Mardi Gras, if that’s even a thing in WA). But I imagine some sort of public event chock full of Americana, even a hipster art walk with firedancers, jam bands and fried X on a stick would be fun
As an aside, maybe playing up Easter celebrations in general would be fun. Even if it’s a bit early. Dyeing eggs (maybe even attempt some pysanki), egg hunts, baskets of goodies, a nice traditional Sunday dinner.
Any indoor water parks or kiddie casinos near you?
Monster truck rally/tractor pull? VERY 'mercan.