New York City has a few nick names, for example "The Big Apple", "The City That Never Sleeps" and "The Financial Capital of the World". We cannot list everything that there is to do in NYC, because it is too much. The basics however are the Statue of Liberty, Times Square, Broadway, Little Italy / China Town and the Empire State Building.
Washington DC is the capital of the USA and hosts for example the home of the president ("White House"), the Capitol and Lincoln Memorial. Outside of politics there is the excellent Smithsonian museum.
Niagara Falls are one of the top 3 waterfalls worldwide in regards of size and name. The falls are located at the border between the USA and Canada, west of Buffalo. The Canadian Horse Shoe Falls are the most famous and visited by many tourists and honeymooners.
Las Vegas is the show and gambling capital of the USA. World famous and featured in many, many movies. A wide variety of hotels from budget places to top-class resorts.
The Grand Canyon is really grand. When standing on the ridge of the canyon and looking 1 mile (1600m) down to the river Colorado that created all this, you do owe the river a lot of respect. It is possible to walk all the way down and back up in a day, what can be recommended.
Los Angeles (aka. City of Angels) is the 2nd largest city in the USA and has a lot to offer, including great shopping (a la Pretty Woman), Hollywood, Venice Beach and sports (L.A. Lakers).
Monument Valley is a desert with few small, steep mountains/rock formations in the shape of monuments. The area is a "classic" and must-do in the Western USA. Of course it is featured in many movies...
Nashville is the second largest city in Tenessee and the heart of Country Music. Of course you should listen to the music that inspired so many and visit The Country Music Hall of Fame.