The most popular sports to watch in the USA are Basketball, Baseball, Ice Hockey and American Football, and most major cities have a team in at least one of the leagues playing there. The culture around sporting events in the USA is different to the UK, and the crowd tend to turn up well in advance of the match in order to soak up the atmosphere. Tailgate parties in the car park before the match are popular, particularly on hot days, when you see plenty of barbeques around the stadium.
If you prefer to get involved rather than sit back and watch, then you can do practically any sport you choose in America. The Rocky Mountains have many ski resorts - most notably around Aspen in Colorado. Along the Atlantic coast in Miami and other seaside resorts, most water sports are available such as sailing or wind surfing, while the surfing in Hawaii is world class, and attracts participants from all over the world.
Golf is popular in most US states, and you will find golf courses in most cities, particularly in Florida.