It really depends on what you want to do with your time here...
Times Square in NYC is a great place to see, and a ton of fun, but man, I'm two hours away and it's about the most expensive weekend I could ever have.
Las Vegas is probably your cheapest destination, but since you're from the Netherlands I don't know that you want to spend all that money to visit the closest thing we have to your home
If you're looking for a relaxing time with friendly people, I'd recommend either of the Carolinas. Absolutely stunningly beautiful country to the smallest detail. (Though this isn't going to be a draw - even the medians to the highway I-77 is full of all sorts of flowers - which coming from someone used to CT, NY, NJ highways always makes me go
)
If you have kids, then Florida would be the place to go. Disneyworld, Epcot Center, places to see Manitees in the wild, Seaworld, etc., etc., a million things to do. Decent family plans too.
The bottom line though is that the United States really is a beautiful place with something for everybody. We have the best part of the continent - the one with endless variety
Google picture a few states to see what you like best