Congratulations! We took our kids then 12 & 14, on a cross-country trip in 2007. It was the absolute smartest thing we ever did. We're from Georgia and had never been any farther west than New Orleans, so we were in for a real treat.
We did not make many reservations. I did not feel comfortable overnighting at truck stops or Walmarts with the kids, so we stayed in a lot of state parks, RV resorts, and KOAs. Every day around 3pm I figured out about where we'd be at 5p, called a nearby campground and made reservations for that night. We tried to find places with a pool or lake, so the kids could work off some energy after being trapped in the SUV all day.
My only exception to the no-reservations rule was when we went to Yellowstone. We were having a family reunion, so we wanted to make sure we got the campgrounds and hotels that we wanted. We were there in July and it was pretty packed, so I was glad we didn't take a chance on finding a walk-up site.
DH is disabled with heart/lung disease and needs a lot of rest on the road, so we were never quite sure how far we would get every day. We usually drove about 2 or 2-1/2 eight hour days, then rested for 2 days. Obviously, we didn't get anywhere fast but we thoroughly enjoyed the drive.