Great question! Love it!
These cities have been chosen by you because they are the five to give someone the best understanding of what the United States is all about. There are no other criteria.
If the above is the true criteria, then it would be fun to put together many packages for your travelers. Couldn't cover and explain the USA with 5 of its cities, but could definitely try to give a sample. I am going to cheat just a tiny bit and choose 2 or 3 representatives (big and small cities) from the 4 major subregions of the USA for both city lovers and natural wonders:
Northeast
#1 NYC - what a better introduction to the US other than our biggest and most diverse city that is alive 24/7 and represented in movies, music, etc. It represents the diversity of the USA and also the abilities of man, his skyscrapers/infrastructure, and his creations with incorporation of central park and nature.
(OR)
# 2 Washington DC - our nation's capital and cultural opportunities abound. Represents our government, our diversity again, importance to education, and great monuments/museums for tourists.
(AND)
Portland, ME - see the American lobster fisherman catch his bounty in some of the most beautiful cliffs of the eastern seaboard
Midwest
#1 Chicago - another major representation of the USA and the midwest. The grittiness, the metal, the history of slaughterhouses, the architecture, the taming of the river (to make it run in reverse), the food, baseball are all very representative of the USA in my mind. May not want to pick this one if picked #1 or #2 from the above as you may have gotten your fill of large cities.
(OR)
# 2 Kansas City - again, very representative of the midwest in my mind with barbecue, blues, beer, baseball, progressive gigabit internet, walkability, etc. Runner ups St. Louis and Cleveland/Cincinnati
(AND)
Green Bay, WI - visit to Lambeau field and eat some cheese curds in small town America. Runner Ups: visit the lakes of Missouri
South (very tough category)
# 1 Miami - I think a must see of our melting pot of South American, Caribbean, African cultures. Beautiful beaches. Great food. Interesting nightlife.
(OR)
#2 Atlanta - stronghold of CNN, Coke, African American culture, great foods, and a wonderful city with progressive bike route around town.
(OR)
#3 New Orleans - history, Creole culture and food, jazz/music, southern culture
(AND)
Hot Springs, AK - this is where Bill Clinton is from; every tourist knows Bill! Runner up, Savannah, GA
(I realize I left TX out! I can't decide! But a tourist must definitely visit Texas!)
West (very very tough category)
#1 San Diego - tourist friendly, relaxing, beautiful beaches, great Mexican food, surfer culture
(OR)
#2 San Francisco - tourist friendly, can be relaxing or upbeat, large city, close to wine culture of America, tech culture, diversity
(AND)
#3 Seattle - port city, nothing like the Sound, Mt. Rainier close by, trips out the San Juans, Microsoft/Boeing/Amazon
(OR)
#4 Portland - a friendlier and smaller version of Seattle and PNW culture, weird/quirky, beer central
(AND)
Anchorage, AK or Honolulu, HI - to show the extent of the US empire and the vast geographies that the country commands
Whew! Hope the OP isn't offended by my quick, superficial analysis with some cheating!