We drove from Sacramento area to east coast when our kids were 9 and 11. We had approximately the same time frame you have. We spent 10 days at Disneyworld and had a great time with the road trip. We stayed in lots of state parks, and stayed on the 10 going east and the 40(? through Oklahoma) going west. We always tried to see the National Parks, as well.
When the kids were 11 and 13 we drove north with a turn around point at the Wisconsin Dells. We wanted to play in the water parks, but we were rained out; still had fun. We saw family in Minnesota (and the Mall of America) and stayed in most of the National Parks (Theodore Roosevelt, near Rushmore, Yellowstone, Grand Tetons). That trip was 3 weeks. In the north we saw the headwaters of the Mississippi in Minnesota and the end down around New Orleans; that was neat.
Highlights....Wisconsin Dells (pet lots of baby critters: tiger, cougar, fox, etc...at the zoo that starts with a Tim...), eating local food (caramel cake and bbbq in Memphis, cheese curds in Wisconsin), Destin Beach, Atlantic Ocean (in Florida north of Daytona), finding our chicken in the RV (Az...yes, it was alive and living in the storage under our bed...even laid 2 eggs...ended up gifting the chicken to someone in AZ), WDW, Universal (stayed in a hotel there for a night to get the early pass), feeding burros in Custer State Park, seeing critters in Yellowstone and the Grand Tetons, seeing armadillos in LA, swimming in the Texas state park springs, watching Twister before driving through Oklahoma (haha...our kids think we have a mean streak!)..just seeing the country in general has been great.
My son wants to see all 50 states before going off to college. We are half way there.
Looking forward to another 3 week trip going to Niagra Falls next summer. So, I would like to see what people recommend, as well. This summer we are staying in Ca.
