The US is a big place with tons of stuff to see! Anyone going a long distance, (as you would be crossing the "pond"), I would recommend you stay 3 weeks if possible.
One possible trip could be the Rocky Mountain region. If you like world class museums, one trip you could consider is Colorado including Denver. Several national and state parks are fairly close by (Rocky Mountain Nat'l Park and Cherry Creek State Park).
Denver is in northern Colorado, so you could drive a vehicle to Wyoming and fit in a grand trip to Yellowstone National Park to see the geysers, mudpots, wildlife, etc. Book all lodgings WELL ahead, especially if in summer.