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.
Las Vegas is the show and gambling capital of the USA and the Western world. The city is featured in many, many movies and TV series. Las Vegas is a desert city with water coming from Lake Mead.
The Las Vegas strip is the best known with casinos, fancy hotels and top-class resorts. You can also find the Eiffel Tower, Little Venice, a Pyramid and Lady Liberty here. Of course you can get married here with Elvis Presley as your witness.
The Yellowstone is the oldest National Park in the USA and hosts a wide variety of animal life (incl. bears and buffalo) and vegetation. The natural beauty will make quite an impression. Beneath the Yellowstone there is volcanic activity that causes many hot pools and geysers ("Old Faithful").
Bryce Canyon National Park is a national park located in southwestern Utah. The major feature of the park is Bryce Canyon, which is a collection of giant natural amphitheaters.
Grand Teton National Park is a great park not far from Yellowstone with similar wildlife, but without the geothermical experience.
Zion National Park is one of the great national parks in Western USA featuring geological wonders, basins, rivers and walking ways.
Mount Rushmore National Memorial is centered on a colossal sculpture carved into the granite face of Mount Rushmore in the Black Hills, South Dakota. The sculpture features the heads of Presidents George Washington, Thomas Jefferson, Theodore Roosevelt and Abraham Lincoln.
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.