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First of all, there's an 800 pound gorilla in the room which you've not taken into account. The rear seat of the Mustang is not comfortable for even one relatively short adults for short rides, and you're planning on putting two college-sized people back there for at least a week. That is not going to make for a fun trip. Still, I suppose it's possible to make the trip with frequent stops and changes of position, spreading the pain. You'll need at least a week for the general route you've described. As a very rough guesstimate of the cost, I'd say at least $1500 just for the one week, one-way transit, but that ignores the cost of any attractions that require an entrance fee or the cost of getting three of you to California to begin the journey.
The other thing that the four of you will have to decide is the answer to the rest of your questions, You seem to have a basic route in mind. The obvious sights along it are the Pacific Coast Highway, Las Vegas, Grand Canyon, New Orleans and/or Memphis and the Appalachians. Besides those, the places to see and the routes to connect them are entirely up to you all. There is no 'best' or even recommended route. The point of a RoadTrip after all is to have the freedom to do what you want, not what some tour director tells you to do. So have a sit down with everyone involved one evening and go over some maps and basic routes. See what your friends want to do and then start connecting the dots. Once you've figured out where your interests lie, then maybe we can help you with some lesser known venues. But there really is no 'middle of nowhere' anywhere on your route.
AZBuck