Barcelona, because it was totally different from anything I would experience living here, and full of exciting things to do, but at the same time seemed really friendly and relaxed so I wasn't intimidated at all. And my trip there just came at an all-round good time in my life. For a specific place, probably Park Guell in the north of the city would be the coolest.
It's one of the oldest cities in Europe, and it was mostly untouched by WWII. As such, there's a huge variety of beautiful architecture, some of it dating back to the 12th century, most of it in good condition.
The Czech Republic is still recovering from the effects of communism. It's still a poor country, by European standards. That's too bad for them, but it makes everything pretty cheap, even in the areas frequented by tourists. The country is also on the rise, economically, so you don't see much depressing poverty (though I'm sure it still exists outside the cities).
Prague has more bars per square kilometer than any other city on earth. They have good beer, and you can buy a liter of it for a dollar and some change. The food was really good, too.
Everyone I met was really friendly, and there was very little of they hypocritical anti-Americanism you see in other European countries.
Machu Picchu. Absolutely beautiful, also an invigorating hike. One of the few places I've traveled where the people there were not the best part of being there. I wish no one was there, but of course there were hundreds of tourists.
