I have done several cross country drives (LA-CT, CT-SD-CT-VA, VA-SF, SF-VA), all of them solo. The best advice I can give you is no mater where you are starting or ending, new Orleans is on the way. A night or two on Burbon St has been my rule of thumb. Highly recomend following this plan. Other than that, get off the Highway when you can to see the local sights. I will never forget the looks I got pulling into a gas station in the middle of OK somewhere at 0630 AM on a Tuesday, all hopped up on strong coffee, smoking a huge cigar and blasting Techno in my bright yellow P5. It seemed like the locals were not sure what to think, untill the saw that I had California plates on the car. Once they saw that they just sort of shrugged and moved on. It was classic. Seriously, make rough plans, but be ready to change them for if you see anything worth checking out. I once was driving accross the country on my birthday. i spotted a sign for a BBQ dinner that was being put on by the local Fire Department. Even though I was planning on going another few hours i stopped and fit up the BBQ. It made for a great Birthday Dinner. Lots of good times can be had if you remain flexible and keep your eyes peeled.
......Or, you can do it in 4 days (or even 3, BTDT) and see nothing. Ten years from now, which story do you want to tell?