We were in GT, Yellowstone and Glacier this last summer.
GT is certainly the less crowded but because it's the one which is the most visited by hiking.
Yes, Yellowstone is crowded, but essentially in the highlights(Geysers, yellowstone river, mammoth...) but you can find solitude hiking(imperial geyser, lone star geyser, south rim of the yellowstone canyon,...) and even in the highlights
quietness could be found if you lodge in the parks...old faithfull after 7 pm is not like OF at 4 or 5 pm...
Finally, out of Going to the sun road which could be a jam...Glacier is a quiet park, as it's a hiking park...there are some very heavy traffic in some trails(Hidden lake overlook, Iceber lake) but the others trails offer solitude and wildlife and even the 2 above are so scenery that you could forget not to be alone...
With teens, an experience in those parks is unforgettable.
Erik
PS : you have to reserve early in advance to find lodging in those 3 parks

There's a reason both Yosemite and Yellowstone are crowded in the summer. This is the best time to visit them. There's a lot more to Yosemite than Yosemite Valley and to be able to enjoy the high country in good weather, you need to go from late June through September. Yellowstone is the same altitude and that's the best time to visit as well.

If you can go in early July, you will find the Parks a little less crowded than later in the month or in August. Or, if you can go to Yellowstone in late August, after school resumes, you will also find it less crowded.

Both parks are outstanding and represent the best of what the US offers in the way of natural scenery and alpine grandeur.

If you are moving to Canada next year, you can look forward to some other great National Parks in the Rockies and British Columbia. The glaciers up there put the ones in the US Glacier National Park to shame.

For more info about the US National Parks, there is an excellent article in this month's Conde' Nast Traveler:

http://www.concierge.com/cntraveler/articles/501351

Thanks emmaloy! We went to Acadia this summer for the first time and loved it and have been to many on your list, excluding Utah. Clearly Utah needs to be high on our list for future vacations! Thanks.