I'm not an expert on the east coast, but I'd suggest something like starting in or near New York City, head down the eastern seaboard to Florida and catch maybe Miami or Orlando, then come across I-10 which will take you along the gulf coast; maybe get to see the state of New Orleans... Go through Houston, San Antonio, across southern Texas to El Paso, head north on I-25 to Denver, then head west on I-70 through Utah and catch Zion National Park (as Erik suggested), Grand Canyon, Las Vegas, drive through Death Valley, head up highway 395 to catch the Sierra Nevada, Yosemite, and then drive across to San Francisco.

With that, the major things you'd miss would be Chicago, Seattle, and Los Angeles.

Keep in mind that there's relatively little to stop and see between about New Orleans and El Paso, and that's true regardless of where you decide to cross the country. Either you get stuck driving through southern Texas (which isn't too bad, there are some somewhat-interesting mountains, etc. after San Antonio) or you'll have to drive across mid-Texas on I-20 (boring!), do I-40 through Oklahoma, panhandle of Texas, and New Mexico (pretty boring!), do I-70 through Kansas (awful!), or I-80 through South Dakota (a little better), or I-90 or I-94 (never been down either of those, but I don't *think* there's much to see up there).

I personally have a strong bias to the southwest. I'd personally check out NYC, Washington DC, and then pretty much high-tail it out to the southwest: Southern California, Arizona, Utah, and Colorado. Not that other areas don't have a lot to offer, but when if you enjoy the outdoors, the southwest of the U.S. is a 'target rich environment'. :) I'd also think that this is the area of the country would be the most different from the UK.

Regards,
Craig Steiner