Welcome to the forum and congrats on your new RV.
I can't give you any advice on which route to take. I would just check Google Maps, or a similar site, and decide where I wanted to go and what I wanted to see.
I don't know if you will be staying strictly at Campgrounds or will be doing some boondocking.
If you are considering some quick 'overnight' stays, don't forget:
Free CampgroundsFree CampsitesCasino CamperThere are other sites, just do a Google search.
When traveling, I like to use
Roadside America. Maybe you can find something of interest.
Personally, I prefer to travel the side roads and US Highways when possible. You can't see America from the Interstate.
Enjoy your trip. And, don't forget to give us a report when you get back. (or while on the road)