I can't speak about Yosemite. I've never been there. I do recall they had a plague outbreak there a few years ago.
Caveats: have bear spray for hiking in the Northern Rockies; when I camped in Canyonlands back in 2000 the camp didn't have drinking water (I was in a tent); it can be hot and windy in Utah in the summer at Arches/Canyonlands.
Pay attention to the calendar...and the weather! The first year I went out West in 1998 I ran into a storm about June 1 and it snowed. Last year in Yellowstone it snowed on Sept 15...pretty chilly in a tent. The Northern Rockies, esp Glacier, can get iffy as you get into September...once it snows at Glacier it's not uncommon for them to start closing some things down.
Also, in Glacier, there are limits on the length of vehicles going over the Going-To-The-Sun-Road. If your vehicle/rig is too long, you have to drive around the park to the south to get to the other side. If you go to Glacier, I would highly recommend staying at the Many Glacier campground on the east side of the park. It is 'wilder' over there, and seeing bears is fairly common, esp in Sept when they are feeding heavily prior to hibernation. In the late afternoon you'll often see people with binoculars or spotting scopes on tripods glassing the slopes of nearby mountains from the Swiftcurrent Inn parking lot looking for bears, sheep, or goats. Just be aware that the road to Many Glacier from Babb isn't the best.
There's a new Cabela's in Kalispell, and you have Big Bear and Scheel's in Great Falls. Bob Jacklin's Fly Shop in West Yellowstone is good if you like to flyfish, as is Blue Ribbon Flies.
Also, pay attention to holidays...Memorial Day, 4th of July, and Labor Day, as they can make finding campsites a problem if you aren't already in one several days before the holiday.
At Glacier, Johnson's cafe in St Mary is always good. In West Yellowstone, Running Bear Pancake House for breakfast and Wild West Pizzeria are good.
If you get a chance while at Yellowstone, take a day trip east to Cody to the Buffalo Bill Museum. There are a number of museums all in one place, including a Plains Indian museum, a firearms museum, and a western art museum. If you pass through Pinedale, Wyoming, stop and visit the Museum of the Mountain Man.
And to reiterate what knight said above, if you are planning to hit a bunch of national parks, getting a national parks passport will save you a goodly amount of money.