As you apparently are from the UK, I'll try to suggest some things you hopefully won't find at home, many of them natural wonders, some cultural wonders, and ignoring your intended destinations. There still are many states that I haven't visited.... You'll have to sort out the best times to visit and plan your itinerary. Some cities and destinations are more economical than others, and yet offer some of the same attractions.
1) Read the "Last of the Mohicans" and see the movie before you come, then visit some of the attractions on the Hudson River, including West Point (see the movie "The Long Gray Line"). Read Meacham's "Franklin and Winston" before visiting Hyde Park.
http://www.hvnet.com/
http://www.westpoint.edu/Dcomm/vic.asp
Visit Saratoga, NY, where the Americans made possible their eventual independence from Britain by destroying an invading army and thereby luring France into a world war against Britain. Saratoga also once was the summer playground for America's wealthy and where the potato chip was popularized. Fort Ticonderoga, the "Gibraltar of the North," and the beautiful surrounding region additionally might interest you.
http://www.nps.gov/sara/historyculture/index.htm
http://www.americanrevolution.org/hessians/hess15.html
http://www.pbs.org/ktca/liberty/popup_vonriedesel.html
2) Allow for two days at Niagara Falls. Be certain to take in all of the attractions, including the jet boats. It's relatively cheap.
3) Continue to explore the Great Lakes and their freshwater shores with visits to Presque Isle near Erie, Pennsylvania, especially if there in August when Lake Erie soars above 75 degrees Fahrenheit (get used to Fahrenheit).
4) Visit Cleveland, the "new frontier" just two centuries ago, and the wealthiest city in the world on a per capita basis just over a century ago (many great American industrialists, including Rockefeller, had their roots in the city). Enjoy a baseball game at Progressive Field, one of the best new baseball palaces in the U.S. The first rock concert ever was held in Cleveland in 1952 (the Moondog Coronation Ball), and it's now the home of the Rock 'n Roll Hall of Fame, an architectural gem even if you're not interested in the music. Visit the "Steamship Mather" and the U.S.S. Cod (a lake iron ore carrier and the last unmodified U.S. WWII fleet submarine, respectively). Cleveland has one of the five best art museums in the U.S. (admission is free) and one of the best orchestras in the world, with renown venues at Severance Hall and Blossom Music Center. The Mormon Church was organized in nearby Kirtland, and this history is recreated in historic Kirtland (if you're interested in divine revelations, this is the American Mecca; the spiritual nature of the U.S. often is not seen or grasped by visitors). Near Kirtland also is the Holden Arboretum, one of the largest in the U.S. and a great introduction to the flora of the northern U.S. Amish communities are located south and east of Cleveland. A visit to Cleveland is much cheaper than many other destinations in the U.S.
5) A hidden Hollywood mecca and a great window into American agriculture is located a couple hours south of Cleveland at Malabar Farm. Try to visit Columbus on an Ohio State football weekend. Obtaining tickets to a game might be prohibitively expensive, but Skull Sessions before the game are free (just get there early). The rituals and pageantry surrounding an Ohio State home football game are as spectacular as the changing of the guard at Buckingham Palace.
http://www.bookthink.com/0078/78brom1.htm
http://tbdbitl.osu.edu/?action=a075
http://jimtressel.com/tradition/block_o.asp?section=tradition
6) Dayton, Ohio, is the mecca of aviation history. The first real airplane is housed there at Carillon Park, the field where the first plane was flown is preserved, and the U.S. Air Force Museum dwarfs any other military air museum in the world, housing even retired presidential airplanes which visitors can walk through.
http://files.asme.org/ASMEORG/Communities/History/Landmarks/5661.pdf
7) Other Ohio attractions include Cedar Point, the world's top-rated amusement park and the roller coaster capital of the world, and "The Wilds," a 10,000 acre wildlife preserve. While at Cedar Point, be certain to visit Put-n-Bay and the Perry Peace Memorial (only a century ago, Americans were conscious of and still grateful for the miraculous peace that reigned in North Ameriica with the largest undefended border in the world; check renovation schedules).
http://www.lake-erie.com/
8) Visit The Henry Ford in Detroit, including the Ford Rouge Plant Tour.
http://www.hfmgv.org/
9) Other Michigan attractions include the Mackinac Bridge, Soo Locks and the beautiful eastern shore of Lake Michigan.
10) In Chicago, be certain to visit the Signature Lounge atop the John Hancock Building.
11) South Dakota: Mount Rushmore.
12) Banff National Park in Alberta.
13) In Alaska, Kenai Fjords National Park and the train to Denali.
14) Yellowstone in Wyoming, a geothermal and wildlife bonanza. Allow at least three days IMO. Best to avoid the summer (June1 to Aug. 31), when families vacation. This is true of many of the national parks.
15) California: Yosemite National Park in May or June (when the falls still are full of water). Hearst Castle, spring at Death Valley (it's spectacular), Monterey Bay Aquarium, San Jacinto Tramway in Palm Springs, Long Beach (Queen Mary, Aquarium of the Pacific), Napa Valley. Try Tri-Tips grilled over redwood outdoors.
16) Arizona: Grand Canyon, Oak Creek Canyon and red rock country of Sedona. You only need one day at Grand Canyon. Get to some other national parks in the Southwest, especially IMO Bryce Canyon in Utah:
http://www.pigseye.com/mc/4corners
17) Biltmore Estate in North Carolina.
18) Charleston, South Carolina, one of the few cities in the South not destroyed during the American Civil War.
19) New Orleans, especially during Mardi Gras. Sitting in Antoine's or visiting the Cafe du Monde late at night are magical experiences IMO.
20) Antietam in Maryland was the site of the bloodiest day in American history and is very hallowed ground. It was the precedent for the beginning of the end of slavery in the United States. Gettysburg, Pennsylvania, is the site of the greatest battle in North American history and one key place where the United States was preserved. Standing on Little Round Top sends chills through many Americans. Read the "Killer Angels" or see the movie, "Gettysburg." Many historians view the American Revolution as the second great civil war among English-speaking peoples and the American Civil War as the third and last (e.g., see Kevin Phillips, "The Cousins' Wars").
21) Williamsburg, Virginia, is a place stuck in time, and evidence of the extreme wealth of the Rockefellers and its philanthropic use. It's also a glimpse into British America.
22) Baltimore, with Fort McHenry, a great railroad museum and the National Aquarium.
23) Boston with the U.S. Constitution, great cultural institutions, and history galore. Visit Harvard in nearby Cambridge. Visit Minute Man National Historic Park, where the United States was born and popular democracy began its renaissance.
You should consider joining the American Automobile Association. Its trip planning services and materials and their membership discounts would save you a fortune. These services may be available through a reciprocal arrangement with your automobile association, but I'm not certain if the discounts would be honored without an AAA card. Use Expedia.com for lodging discounts. Local AAA offices may be a cheap place for currency exchange. A GPS system would be invaluable, but AAA maps and state guidebooks would help you immensely.
http://www.aaa.com/aaa/sem/sem.htm?redirectto=http://www.aaa.com/?area=JoinSEM&skin=JoinSEM&gcid=S15141x073&keyword=exact_aaa
http://www.aaa.com/aaa/sem/sem.htm?redirectto=http://www.aaa.com/?area=JoinSEM&skin=JoinSEM&gcid=S15141x073&keyword=exact_aaa
Make certain that you have auto insurance that covers rental cars in the U.S. & Canada so that you don't have to pay insurance on every car that you rent. You can get insurance through AAA. Enterprise rental cars usually are the cheapest and they deliver them to your hotel.
BOL!