Ironnerd:
Definitely buy a US National Park Pass. Visit the big 5 Parks:
- Yosemite -- Hike the Valley, the Mist Trail, and in the woods for Sequoia Trees. Climb up Half Dome, take in all the waterfalls, and exit to the east through the Sierras.
- Grand Canyon -- Check out all the viewpoints. Hike to the bottom for a whole different perspective.
- Olympic -- Pacific Beaches, glacier lakes, mountains, rain forests, cougars, and more.
- Arches -- Delicate Arch is a beautiful hike and park is full of arches and other beautiful rock formations and wide-open vistas. Ride a mountain bike in Moab.
- Glacier -- Check out the Many Glaciers area and drive the Rising to the Sun Highway. Ride you bike when allowed. Lookout for the Grizzlies, mountain goats, and big horn sheep.
Also, look at all the other parks, monuments, and whatnot that make up the Parks system. You can climb up a Lighthouse and see where the first successful motorized airplane rides took place at separate sites all within the same morning in North Carolina.
There lots of hiking opportunities on The Pacific Coast Trail, The Appalachian Trail, and Continental Divide Trail, and even old train track trails coming together in the Midwest. You don't have to hike the whole distances, but you get to see some beautiful scenery away from the highways and freeways, all for free.
Drive through Monument Valley in northern Arizona.
Visit the wacky/tackey tourist stuff:
- Cadilac Ranch in the Texas Panhandle
- Corn Palace in South Dakota
- Museums of stuff you did know existed, with most in places you didn't know existed.
- Visit the Indiana High School basketball Hall of Fame in New Castle, Indiana that is beside the largest high school basketball gymnasium in the world.
- All sorts of money grabs of firsts, the biggest, tallest, smallest, and any and all sorts of things, found "just off the highway."
Experience Seattle. Arguably the prettiest city in the world when the sun is out. Visit the Space Needle and you'll see Mt. Rainer, The Cascades Range, Puget Sound, and more all at the same time. Enjoy the great vibe and food and entertainment. Ride the Ferries to wherever in the area.
Bring your gear and race in a small, independent triathlon. Volunteer in another. Feel first-hand how welcoming Americans are to others.
Ride the subway in New York City, The El in Chicago, and the BART in the Bay Area.
Visit old mining areas in northern Minnesota (iron ore), Colorado (gold, silver, copper, and more), in Arizona for metal ores and gems, and in Bisbee, TX.
Cruise on a boat in the Mississippi, Ohio, Missouri, or Hudson Rivers. Sorta like being on one in the Murray River back home.
Boat out to some of the islands: Catalina off the Southern California coast, the Manitou Islands in northern Lake Michigan, Mackinaw Island in northern Lake Huron, of the 10,000 Islands in the St. Lawarence Seaway out east.
Go canoeing in the Boundry Waters (BWCA) of Northern Minnesota or use a power boat in Voyageurs National Park (sorta) nearby. Or visit lakes in Minnesota (there's over 10,000 of them) or possibly prettier ones in Michigan or Wisconsin.
Visit the wine areas in Northern California, eastern Washington, southwest Michigan, the Fingers Region in New York State. Compare to OZ.
Listen to FM
AND AM radio to get a sense of the country's politics, religion, agricultural, and more influences through the different parts of the country.
Check out any or all the war memorials in any small town in the country where they honor those who served in various wars with many making the ultimate sacrifice for their country, and others including Australia in WWII.
Attend small town holiday parades for Memorial Day in May, the 4th of July, or Thanksgiving Day in Nov. Alternatively, attend parades for special seasons/occasions including whatever small-town festival or homecoming event is happening. That's the real Americana.
Participant in a State Fair. Iowa and Texas are huge, but any state will do for the uniquely American experience.
Bill Bryson got an earlier shout out for Australia feel. He also wrote two good books worth buying for American walkabouts and driveabouts: "The Lost Continent: Travels in Small-Town America" and "A Walk in the Woods: Rediscovering America on the Appalachian Trail", to get a feel of away from the city America. (and in the spirit of Bill Bryson, I wrote a book about a triathlon journey in all 50 states that may provide you with some additional ideas about what to experience during visit here: "Triing: A Journey of discovery, challenges, and camaraderie while racing in 50 states and the continents beyond" Available on Amazon).
And just maybe, grab some grub at a small-town store and head to the local city, county, or park/forest preserves. Eat, walk, listen, dream, fall asleep for one of the most relaxing, cheap, and delightful days of your journey.
And finally, as long as your spending money into the country's economy and not causing any issues, there's no need to apologize as you will be a net positive for the immigration and homeless metrics.