I grew up in Burbank, California, but all of our relatives were on the East coast. Every other summer we would spend six weeks camping from coast to coast. By the time I was nine, my parents assigned me the tasts of trip planning and navigation. We mapped a different route each time depending on the time of the summer that we went. One year the trip was in late May, so we took the southern route and saw the petrified forest, the Grand Canyon and the desert southwest. Texas and the Alamo, Louisiana and New Orleans, then the Everglades, then up through the coastal states to Virginia and Maryland, where the realitives lived.
Mid-summer, we traveled the middle of the country, first through the Sierra Nevada mountains, then through the middle of the country to the East coast. The mountains are beautiful - Flagstaff and Breckenridge are two of my favorite places on earth.
High summer - the Northern, and my favorite, route. Up the California coast through Washington and Oregon, through Montana, then onward to the Great Lakes, then south through New York, stopping to see a few of the landmark sites, then south to Baltimore and Washington D.C., with a few day trips to Williamsburg/Jamestown and lots of time at the Smithsonians.
One year, we went late summer and did all of New England, traveling south with the leaves changing. Absolutely wonderful trip.
I envy your ability to do this - someday we will have enough time off to do this. Plan ahead, make reservations at the campgrounds so you don't end up sleeping in a field in Montana (although it was kind of fun). We traveled (all eight of us) in a station wagon with a pop-up, and it was always interesting. Take your time, plan some side trips and don't plan on too many miles in a day. We usually took 10 days across the country, ten days back and lots of time in the middle.
Most of all, pack your sense of humor and more money than you think you'll need. We always had some mishap. Anyone remember Firestone 711 tires? We managed to blow several on one trip. Water pump failure in the middle of Kansas. We found a garage that was willing to work on it after hours on a Saturday, and spent the afternoon having root beer floats at an old-time soda fountain in a small drugstore. Don't buy souveniers at the tourist destinations - go to the nearest Walmart and get T-shirts from the area. In D.C., do the opposite - the T-shirt vendors around the Mall have cheap shirts.
Happy Camping!