Freedom to do as you please.
Hello and welcome to the RTA forums !
With a trip acorss much of the country with no time constraints means you have thousands of possible routes and attractions to choose from. The "ideal route" would be the one that takes you where you want to go based on your interests, time and budget, so I would make a start by doing a little research by digging around the RTA site [where you will find lots of great info] with a good map of the US to hand. Once you have added a few more dots to the map, [like you have the Grand canyon ] then we can start to offer some meaningful advice, but for now there is just too much out there and too little to go on.
2WD will be fine just about anywhere you want to go, as long as you are not planning on any serious 'Off roading'.