Thoughts from a cross country traveller
My wife and I have both done the cross country thing enough to probably have been half way around the world, but I still love it. But, we still have yet to do it together...
Anyhow, a couple of small thoughts. You may want to do a there and back deal if you have the time and money. The north and south are so different and there is a lot to see on each side. As has been suggested, try and take smaller roads. But, even in the mountains there is nothing to worry about. Honestly, you may find the smaller roads in the mountains offer more places to see and stop than the highways. I'm just thinking of outside of Denver, where I find taking US40 is a lot more enjoyable than I-70.
While visiting the major cities can be fun and all, you will find that the mid-majors tend to be a bit more friendly to the traveller, but that really depends on what you are looking for. When I did western Europe, I spend a coulpe days in each major and a bunch of midmajor cities to get a feel for the place. Next time I know wher to go again (Norway, Sweden) and where not to go even if someone offers to pay me (France, Belgium). Plus I feel like I got to see a lot more than I might have otherwise.
If driving doesn't work out, you may want to consider
AMTRAK. While she doesn't compare with some of the European trains, she does outclass a few. But, I would rather drive, and I'm guessing you would too.