Road trip

I am planning a road trip from Alaska to the East Coast at the end of July, and I'm asking for some help with activities and things to do in the National Parks along the way. I have only ever been to National Parks in Alaska, so I am not very in tune with how most of them are set up, what the rules are, or how they work. Any good beginner information would be greatly appreciated.
I am fully aware that it will be the busy season in a lot of these locations. For the most part, I am trying to get out, do hikes, and see the landscapes and wildlife—not just stop into the visitor centers. I would like to try mid-range hikes, around 5 to 10 miles, if the parks offer them.
I will be stopping at:
Banff (and maybe Yoho and Glacier in Canada)
North Cascades
Olympic
Mt. Rainier
Crater Lake
Redwoods
Grand Tetons
Yellowstone
Badlands
I know this is a crazy long and pretty much 'once-in-a-lifetime' kind of trip, so if anyone has any specific stops or trails they recommend along this route, I would love to hear them!