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.
Seattle is a seaport and the biggest city in the North-West. Also the home of Microsoft , Boeing and Amazon. From here it is easy to the Rocky Mountains or to Vancouver, Canada.
Glacier National Park is an American national park on the Canada–United States border, adjacent to Waterton Lakes National Park in Canada. The park encompasses more than 4,000 km2 and includes mountains, more than 130 lakes, various plants and hundreds of species of animals.
Grand Teton National Park is a great park not far from Yellowstone with similar wildlife, but without the geothermical experience.
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.
Chicago, on Lake Michigan, with nick name The Windy City, is one of the largest US cities. The Sears Tower is one of the tallest buildings in the USA.