Not so much cities but what must be seen in the USA:
The Grand Canyon /// http://en.wikipedia.org/wiki/Grand_Canyon
Mount Rushmore /// http://en.wikipedia.org/wiki/Mount_Rushmore
Crazy Horse Memorial /// http://en.wikipedia.org/wiki/Crazy_Horse_Memorial
Las vegas /// http://en.wikipedia.org/wiki/Las_Vegas
Redwood National Forest /// http://en.wikipedia.org/wiki/Redwood_National_and_State_Parks
New Orleans Mardi Gras /// http://en.wikipedia.org/wiki/New_Orleans_Mardi_Gras
Bonneville Salt Flats /// http://en.wikipedia.org/wiki/Bonneville_Salt_Flats
St. Louis Gateway Arch http://en.wikipedia.org/wiki/Gateway_Arch
Mesa Verde National Park /// http://en.wikipedia.org/wiki/Mesa_Verde_National_Park
Meteor Crater /// http://en.wikipedia.org/wiki/Meteor_Crater
Alcatraz Island /// http://en.wikipedia.org/wiki/Alcatraz_Island
Yellowstone National Park /// http://en.wikipedia.org/wiki/Yellowstone_National_Park
Walt Disney World /// http://en.wikipedia.org/wiki/Walt_Disney_World

The Pentagon /// You can actually visit but need to supply passport and information in order to be invited for a visit

World Trade Centre Memorial /// http://en.wikipedia.org/wiki/National_September_11_Memorial_%26_Museum

Durango Train Ride /// http://www.durangotrain.com/
Seven Falls /// http://en.wikipedia.org/wiki/Seven_Falls

Go See a MLB, NBA, MLS, NHL game

Millions of things to see in the USA..... and don't forget to play pinball along the way.