Saying you want to see what life here is like a Martian saying he wants to see what Earth is like -- you can't see it all, especially in a week. The U.S. is so large and culturally diverse that most Americans do not know what the entire country is like. It can take three or four days to drive from one coast to the other.
Where specifically do you want to see in the U.S? Most Europeans I have met head straight to New York. It's certainly an experience, but New York is very different from the rest of the U.S. Other popular cities, such as Miami, Las Vegas and Los Angeles, are also very different, both from the rest of America and each other.
When I visit another country, I prefer to stick to one region and just see as much of it as I can. For instance, the Northeastern U.S. (running from Virginia to Maine) is the closest to Europe, and thus the oldest and most densely-settled part of the country. You can get a pretty good idea of how that part of the country lives, mindful that there are many, many, many parts of the country that live totally differently and are some distance from there.