The size and diversity of the United States is hard to fathom unless you take time for a cross-country drive. A train trip might do, but a passenger train (usually) travels all night, so you miss seeing those parts of your journey. Flying gives a nice overview (is this a pun needing pardon?) but is not the same as driving. Pick an interstate highway (e.g., I-40, I-80, or US 50) for the backbone of your trip, but take time to make side trips to see national parks and other attractions. It takes time and energy, but it will be educational and fun, if you are of a mind to enjoy it. Natural scenery and tourist attractions aside, the article linked below gives you an idea of the amazing geographic diversity you might see.
A Cup of Brouhaha 