Daddy...that would be a heck a lot of fun that is for sure! I have actually always wanted to drive across the country..see the sights...would be a lot of fun!
If you DO go cross-country, ABSOLUTELY be sure you go to the Kansas Cosmosphere in Hutchinson, Kansas... it's one of the BEST space museums I've ever been to. They do a lot of restoration work as well (Gus Grissom's "Liberty Bell 7" was restored there after its retrieval from the ocean floor a few years ago, and IIRC the F-1 remains from Apollo 11 brought up by Jeff Bezos are being restored there, as well as lots of other stuff-- they have a "viewing gallery" where you can look into the workshop at stuff being restored-- they had some V-2 remains salvaged from off White Sands Missile Range being restored there the last time I was there... Plus they have a Titan II out front, an SR-71 you walk under as you enter (and can walk around and view from the top via the balcony walkways around the building perimeter inside) and lots of Russian stuff as well... including a Lunokhod and Svetlana Saviskaya's Orlan space suit, among other stuff...
If you're in the southwest, I recommend the National Atomic Museum in Albuquerque, New Mexico, and the White Sands National Monument and White Sands Missile Range museum and rocket park at the entrance to WSMR on the western side of the Tularosa basin. If you're farther west (and I want to go there myself some day) there's the boneyard bus tour at Davis-Monthan AFB, and the Titan Missile Museum nearby close to Pima AFB, where you can go into a Titan missile launch complex and silo, complete with missile. (Where they filmed Star Trek First Contact). Of course there's "big holes" like the Grand Canyon and Royal Gorge which Daddyisabar might poo-poo, but they're well worth the effort to see-- absolutely stunning! A drive up Pikes Peak is worth the trip alone, despite it being "just a big rock" according to some.
If you're travelling cross-country, I suggest taking the 'northern route' home through the Midwest, up through Nebraska and Iowa and Illinois, Indiana, Ohio, and Pennsylvania. If you're interested in big machinery and factories and stuff, or farming at all, there's the Caterpillar Lexion Combine Plant in Grand Isle, Nebraska... there's also the SAC museum at Offut AFB near Omaha, which I want to get to some day. The Kinze planter and grain cart factory just off I-80 near Pella is very neat, and the National Farm Toy Museum in Dyersville is pretty cool... as well as tours of the Ertl and Spec-Cast factories there. In the Quad-Cities area of Moline, Illinois near the Iowa border, there's the John Deere combine plant, and the John Deere Pavilion downtown-- nice museums, eats, and the combine plant tour is amazing if you like big machinery and seeing how they make stuff from bare, raw steel and then ship it all over the world. Lots of beautiful farm country in between all this stuff. In Indiana, there's the Academy of Model Aviation national headquarters museum and flying field near Muncie, which has hosted some national rocketry events such as the National Sport Launch a few years ago, and they have a nice model airplane museum there. Of course it's only a couple hours drive to Dayton, Ohio and the National Museum of the US Air Force, which is free... plan on spending AT LEAST a full day there... AMAZING place-- get there early and get in line for the tickets to the Presidential Air Force One hangar and the X-planes hangar-- INCREDIBLE stuff in there, but it's inside the protected area, and thus you MUST get a free ticket with the proper ID to board the bus at a pre-scheduled time for the hour or so they take you inside the fence and then turn you loose inside the hangar. I spent a whole day basically just snapping pics as fast as I could going from one plane to the next to the next and spent VERY little time reading the informational displays, and BARELY got it all in-- got the X-planes hangar but only a cursory view of the AF1 hangar next door. Don't forget the outdoor displays as well... some amazing planes out there, as well as a mobile ICBM transporter and a Minuteman missile rail car. Dayton of course also has museums about the Wright Brothers as well.
Get you some Amish cheese and stop in Hershey on your way back to NJ through Pennsylvania, too... hard to beat a good home-style Amish meal and some Amish cheese and of course Hershey has that interesting chocolate factory...
Later! OL JR