3 years ago, 10 weeks with our two dogs and lots of camping and hiking and a backpacking trip at about the halfway point. More casinos than I care to admit. 
We started in Atlanta, going across the south to the southwest, up California through Oregon then eastward to Montana and Glacier Nat’l park, a few weeks with my mother-in-unlawfulness in N. Dakota, thousands of half naked lesbians at the Michigan Women’s music festival, and back down to Georgia.
ETA: I forgot I uploaded a route map
One of the most gloriously stupid things I’ve ever done was get from the Seattle area to D.C. in about 50 hours. My route, roughly, was 90 east to something south (Chicago, I think) to 70 east. Driving through the mountains was gorgeous. I recall that pretty well. Then somewhere in South Dakota, I think, it starts getting flat, and it’s all a blur after that. I pushed myself as much as I could, and when I couldn’t keep my eyes open any longer, I’d pull over for a couple hours of sleep. Toward the end I started hallucinating a bit.
Aside from the stupidity of pushing myself like that, it was compounded because I had many days to make the trip. I just don’t like driving long distances much, and I had my dog with me, so I really wanted to get it over with.
I’ve kinda done it. Took me two legs: Houston to Los Angeles with my parents when I was a kid, and about 6 years ago, Houston to Orlando.
In 1997, with five weeks of paid leave stored up, I got in the car and drove and drove, some 18,000 kilometers in all. Visited:
Montreal (start point)
New York
Washington, DC
Savannah
Orlando
Fort Knox
Huntsville
Chicago
Mount Rushmore/Crazy Horse/Custer’s Last Stand
Seattle
Vancouver
Edmonton
Calgary
Vulcan, AB
Red Deer, AB
Geraldton, ON (where my sister then lived)
Toronto
Hamilton
Niagara Falls
Buffalo
Cornwall
Montreal
Along the way, I visited numerous space and science museums. The longest single drive was down the east coast from Washington, fueled by a number of caffeine pills I’d picked up in a U.S. Military PX and were new to me. I still have all the postcards I sent back.
Single coolest moment of the trip: watching the launch of the Cassini probe.
Biggest regret: not going to Vegas.
Yes, but I was 4 years old, with 4 siblings and 2 parents, in the back of the old white Chevy station wagon.
I do recall touching snow for the first time (we drove from Florida to San Francisco and back, taking 2 different routes). I also recall staying at Holiday Inns and looking for the star on the sign.
This may not be much help to you. 
As an adult, I have driven from Chicago to Boulder and (separate trips) from Chicago to Florida and Chicago to Virginia.
The trips out east are more scenic for longer periods of time. Then again, there is something compelling about the vastness of the Nebraska sky. Pack lightly. Make sure your car is in good working order. Don’t speed through small towns…
Show off. 
Last tip:
No matter how many CDs or whatever you think you need for this trip–double your estimate. Not all radio reception is good, and you may well find that once you are out of a major metro area that your choices are severely limited. I found this out myself, driving to Memphis and back last summer. I ended up listening to the farm reports, not being able to stand anymore country or 80s rock, and NPR not having good reception…
Just get Sirius. Two channels of NPR, 100 channels of music, 4 comedy channels, BBC, CBC, Howard Stern, more sports than you can shake a stick at, CNN, CNN Headline News, traffic and weather in all major markets . . . and it works everywhere in the country.
Now go up to the North Pole so you can walk around the world in a few minutes.