Driving across the country is freaking stupid. There is only so much corn and flat roads that a tourist can take.
Did some work between the the west coast of Florida to Mobile Alabama for a couple of months for my company. Honestly wasn't too bad. Use to live up around Lake Placid along with West Virginia and the Northeast isn't bad. In total over the years spent a good 8 weeks in Utah, always over 2k on the rental vehicle driven out of Vegas and I still didn't see everything I want to see. Last summer, we flew into Sacramento and traveled the Sierra Nevada's, 2 weeks, about 2,300 miles on the rental vehicle and only saw a small portion of the state and loved every minute of it.
I've driven from Pennsylvania to Idaho and Montana a couple of times foir whitewater kayaking.
"There is only so much corn and flat roads that a tourist can take"? Will agree, that central US is not my cup of tea, because yes, it can be flat (we would take our trucks, drive non stop to Montana and Idaho, 2 man driving shifts and luckily for the midwest, I did a lot of sleeping in the truck bed LOL). Yes, generally when I travel, I'm more than happy passing up on the mid west, but that's just me LOL
That said, there is so much to see of the US driving, but only way to do it IMO.
A lot of my drives were when I was single and car / truck camping. Could pretty much go no stop. Last year in California, it was planned for 2 weeks for our family, and I thought what the heck we're we going to do for 2 weeks only being in Northern California? Those two weeks went fast. Also, when you're traveling as a family, you need to rest as even long drives can take it's toal. Drive 15 hours non stop, sooner or later you're going to get to the age where you actually just need a day of rest doing nothing to regenerate your batteries.
Although 3 weeks may seem like a lot of time, if you're flying from England to Florida and then planning to get to Arizona, 3 weeks is actually not very much time to "stop and smell the roses" so to speak IMO.
If you're going to Arizona, for 3 weeks, I'd just fly to Arizona and check out Nevada, New Mexico, Utah and Colorado. Everyone talks about the Grand Canyon, but I'll take some other spots out there over the Grand Canyon any day.
I'm more in the line of 1942willys thinking.
Keep in mind, I'm not a "crowd" person. Believe me, you'll see them at the theme parks in Florida and the Grand Canyon LOL That said, depending on the month in the year will really determine how bad / crowded the popular tourist spots are in the US. Last year took my son up to Niagara Falls on a "NY trip" and luckly we went in the middle of the week end of the summer. It was crowded, but I was told it's 10 times more popular around the holidays. We went to Yosemite in August. We started early by driving to fresno the day before and paid for a tour. It was packed, but manageble because we go there early. 600,000 visitors in the month of August pretty much ensures if you go on a weekend in August you're screwed because you won't even find a parking space (yet another reason we took a guided tour, we didn't have to deal with parking).