Since your heart is set on the USA and you have a limited number of vacation days,
you should try to hit the crowd-pleasers. However, keep in mind that most big cities are very expensive.
Try to do and see as much as you can in those short seven days. Depending on your budget, hit either of the coasts.
So, do New York and Washington, or San Fran and LA.
Or hit the south and visit New Orleans, since it’s the perfect combination of urban culture, landscapes and history.
It all depends on what you’re interested in, really. What would you like to see?