More information on what interests you would help a lot.
Culture is a real problem.... American culture has so many regional and ethnic subcultures associated with it. New York City, Memphis, and Venice Beach might as well be different planets. You have a particular stereotypical "culture" in mind? Southern? North Eastern? Those of Nordic decent? Cowboys? Classic New Yorker (rude, short tempered, and in a hurry)?
I ride motorcycles cross country for many of my vacations. I've seen good and bad everywhere I've traveled. I tend to just travel in a general direction and see what there is to see, with maps and tour guides along. I'll just disappear for 1 to 3 weeks like this, when I can. I'll camp most nights, and stay in motels or bed and breakfast every third or fourth night. It's my favorite (and more affordable) way to see the sights in the States.
Do you prefer ocean and seaside locals?
Do you prefer mountains, deserts, or wide open spaces?
Do you prefer big cities or smaller communities?
Do you plan to do some driving, riding, or making use of a rented Recreation Vehicle (RV-mobile camper)? Do you want to stay in a "base" hotel or hostel and operate out of there to see the surroundings?
Are you into Outdoor activities such Rafting? Kayaking? Hiking? Climbing? Camping?
Do you want to see wildlife as well? Buffalo on the agenda? How about Native American Culture?
Do you want to see some of the big tourist attractions or events? Grand Canyon? Mount Rushmore? Motorcycle Rally at Sturgis or Daytona? Yellowstone?
Make use of the various State Tourists and Local Chamber of Commerce resources. If something about a particular State or City or attraction gets your attention: send away for the brochures. These areas spend good money to create information packets. With them in hand, you can read up on an area's attractions, and better know where to direct follow on research and inquiries.
Also, consider a good mapping program of the States. Or just a big wall map. Start making notes about what you find of interest. You may find a particular area of the States has many of your interests in a reasonably local area.
Personal favorite regions you might want to research for the future:
Asheville, North Carolina. Located in the Southern Appalachian/Smoky Mountains. Friendly, artsy, retirement and outdoor sport community. Knoxville to the west. Blue Ridge Parkway. Southern charm. Biltmore Estate. Probably my favorite area east of the Mississippi River.
Maryland's Eastern Shore. Small seaside villages and farming communities. Find a nice bed a breakfast to stay in. Try to find the Red Roost near Whitehaven (or another good local crab house --- avoid the tourist traps.... get locals to give you recommendations) for all you can eat crab, fried chicken, and Bar-B-Que. Go East to Ocean City for some surf and boardwalks. Go West to Annapolis and Washington D.C. is the Nation's art, monuments, museums, and architecture is of interest to you. College bar near Georgetown for night life if looking for young smart-dumb drunk future lawyers and politicians.
Maine, New Hampshire, and Massachusetts if old sailing history, lighthouses, American's colonial and Revolutionary times is your thing. Boston (although driving there is the worse). Old wooden sailing ships. Arcadia National Park. Rocky shorelines.
Vegas If big city lights, gambling, great food, shows and entertainment are your thing. Sin City has a bit of everything to offer. Beyond the city, Lake Meade, Deserts, Mountains.
Rocky Mountain/Western Experience Colorado, Wyoming, Montana, Idaho, Utah. Tall peaks, climbing, hiking, mountain biking, off road experiences, great outdoors. White water rafting. Skiing. Camping. Big horn sheep, buffalo, mule deer, bear, herds of cattle, cowboys. American West. Yellowstone National Park. Grand Teton. Rocky Mountain National Park. Glacier National Park. Native American Reservations. Ghost towns. Gold Mines. I moved to Colorado because it opened up a big playground for my motorcycle travels.
Left Coast Kalifornia, Oregon. Stay north --- San Francisco or further north. Mountains and Coastlines. Redwood trees. Hippies. The Coastal highway is a great motorcycle ride.
Pre-Packaged Tours For many things, you can take a package deal. For example, there are several tour companies that will rent you a motorcycle, and you follow a tour guide for days to see and do various things, with a chase van following behind to carry extra gear, and deal with any break downs.
AMA Tours for example. There are many others --- leave the hard stuff to the organizers, and get to know your fellow travelers. Best if you don't like to tour alone, or somewhat unsure about any culture differences.
Cruise See Alaska. Fly into Seattle to visit that area (and Vancouver), then take a cruise ship up to Alaska and back. Get to meet many Americans (among others) on-board ship, and see America's last great frontier. Inuit. Eskimo. Old Russian colonial history. Icebergs and Glaciers. Grizzly Bear. Salmon. Kodiak Bear. Seattle, Washington and Vancouver, Canada and the surrounding area are worth a visit in their own right as well.
Florida Disney. EPCOT. NASA. Everglades. Airboats. Florida Keys. South Beach Bikinis. Alligators. Alligators in town. Alligators eating poodles. Swamps. Cypress Trees. Sand. Sand fleas.
Texas, New Mexico, Arizona, and Utah would make for good travel vacations, if you plan on some serious miles or spend a good bit a time researching them. They all contain some gems, but I would not say that planning a vacation in those states is a simple task, and those gems are spread over a wide area.
A big diverse country we've got here.
