What is the food like in Barcelona?
I remember liking it but not many details. They eat very late there. There were lots of tapas (assorted Spanish appetizers) cafes. Lots of fresh produce and hearty breads.
I think you can do Paris justice (i.e. hit all the tourist highlights) in 5 days. If you have no constraints other than length of time I recommend going in late September - October or April - May; the weather is good and you avoid the tourist frenzy.
You should look for nearest and best places nearest to the USA. Places like Argentina, Spain, Netherlands, Azores Island (Portugal) are the places/countries which are the nearest, and you may return after finishing your tour after 6 days.