Good response, TC.
The US is huge and there are SO many beautiful and interesting places. I’ve lived on both coasts and traveled through most of the country and, unlike David_in_taipei who posted above, I DO understand why so many people are in love with California. It’s gorgeous, with 5,000 meter mountains (the Sierras), volcanoes (Mt. Shasta, etc), the world’s biggest trees (Redwoods), the world’s lowest elevation (Death Valley), fantastic beaches, the beautiful Highway 1 going up the coastline, great cities, lush farmland, a diverse population, interesting history (not old by European standards, but interesting nonetheless as it’s long been the golden land to which people traveled to make a new start, or from which great new ideas were launched and fortunes were made).
Other parts of the US are very nice too. New England is great, especially in the Fall. The Pacific Northwest (Washington and Oregon) are lush green and beautiful. Colorado’s great if you want to go hiking or skiing in REALLY big mountains (the Rockies). Other places are also nice.
But if you’re making a first trip to the States, and you’ve got just 2 weeks, I would definitely recommend starting with California as it’s got so much to offer. In the south, San Diego’s a lot nicer than LA. Perhaps if you fly to LA you could then transfer to San Diego and start there. Rent a car and start out with San Diego’s great beaches and beautiful city, with sparkling clean buildings, a stunning bay full of sailboats, a brick oldtown with nice bars and restaurants. If it interests you, SD also has perhaps THE best zoo in the world, Seaworld, Tijuana Mexico just a daytrip across the border (for tacos, margueritas and tacky souvenirs).
Then drive up the coast to LA – Disneyland, Holleywood, etc – and continuing through beautiful coastal towns: Santa Barbara, San Luis Obispo (go see the Hearst Castle there, it’s really cool). Yosemite is surely very crowded in the valley, but it’s got some of the most stunning scenery in the world (Half Dome, El Capitan, Yosemite Falls).
San Francisco is an awesome city, with a gorgeous bay the terrific Golden Gate Bridge (lots of tourists walk across it, as I once did, which is really cool), Fisherman’s Wharf, Chinatown, the cable cars, maybe a tour of Alcatraz prison, and lots of great culture and fine dining.
Continue north through the wine country of Napa Valley and on to the great redwoods and rocky coastlines of Mendocino and Humboldt County. Then fly back down to LA and go home.
That’s what I’d do, but there are lots of other options.