Interstate 90 is the most direct way to get from Seattle to Chicago, and Interstate 80 is the most direct way to get from Chicago to New York. This route is also dull. If you are driving across the country, you should plan a route that takes you to some of the most beautiful places in the West, like Yellowstone, Mount Rushmore, and Wind Cave. This means that you will need to get off the Interstate every so often. (If you don't know what a "Interstate highway" is, you can look it up on Wikipedia and learn more.)
Get directions: mapquest driving directions
The best thing for you to do is join the American Automobile Association, in my opinion. If you are a member, you can get free maps and guidebooks at any of their offices, which are in every town. These include maps and books that list restaurants, hotels, and campgrounds, as well as discounts at those places. You can also get help if you run out of gas or need a tow if you are a member. Without being a member of the AAA, I wouldn't even think about taking a 3,100-mile road trip. You should be able to plan a nice trip for yourselves with the help of your maps, your list of places you want to see, and the places where you can park the RV.
I'll also tell you that even the back roads in the country are at least as good as an English "A" road. We don't have any B or C roads like the ones in England.