America is truly a massive country, not only because of its political, military and economic influence worldwide, but also by its physical size. It consists of 50 states and over 300 million people. It is also one of the most multicultural and ethnically diverse nations. Many immigrants are moving to the country from hundreds of different countries.
As for the climate, there really is no real average, because, given the size of America, it is experiencing almost the full range. For example, Hawaii has a warm to hot climate, with Alaska mostly below freezing. In cities like New York, the summers are quite warm and in winter snow.
Because of its sheer size and variety, it is not possible to mention all the places you should visit in America, but these are just some of the highlights.
A visit to New York is a must. It is one of the most cosmopolitan cities in the world and skyscrapers abound, so you feel really small. Grab the yellow cabin and sail through the streets. Go to the Empire State Building, go through Central Park and take a cruise around the Statue of Liberty. Washington is also worth a quick stop, though only seeing Whitehouse. In Las Vegas, the American course, the parties never end. Go to some of the famous hotels / casinos such as Flamingo, Winn, Hard Rock and Bellagio.
For a little sun and fun, go to Miami and stroll along the beach and admire the summer bodies. Orlando is where you will find Universal Studios, which has attractions that will blow you away. From here it really matters how much time and budget you have. A great idea is to rent a car, preferably a convertible, and drive from Fort Lauderdale (Miami) to New York. This will give you a good ground plan without having to take too long and hopefully you'll also be able to experience and see some of the smaller cities along the road that will help America do what it is.