I loved Italy when I went. Not the big cities, but the smaller ones. Cianciano was really nice, and Abano Terme. The basilicas and the monasteries are absolutely gorgeous.
The only other place I've been was Salzburg, Austria. The coolest part of the short stay there was going through the salt mines, which are kind of a walking museum tour. It included an underground lake and slides to get from one area to the next. There's a castle in Salzburg too, which I don't remember the name of, but if you can get to it the view is amazing.
For people from the US, I think seeing Europe is a great move. Extensively, spend lots of time there, and don't just visit the capitals (eg. Paris, Rome, London etc.), visit the countryside AS WELL. In most European countries, there are trains that go all over the place, so it is not an impossible feat. And you don't need to hire a car. Just get the trains, seriously, you get to look out the window, and see the country as you are travelling, rather than having to watch the road etc.
After Europe, I think either an Asian country (ie. China (countryside), Thailand etc.) Again, venture into teh countryside, don't stay in the capital city. or South America. Particularly Brazil.
I haven't been to an Asian country or South America yet, but they are the next on my list, and I've been reccommended them by many people I know who are avid travellers.
I'm from Australia, and honestly, I don't think it's a 'must see' for you. The USA is basically just Australia, on steroids. You guys just have heaps more people, heaps more houses, and your cities span a lot wider than here. The people over here are a lot different to you all also, but not as different as European and Asian people are.
Canada. I know it doesn't sound that glamorous, but it's beautiful if you go to Alberta or British-Columbia, but not to the main cities. Go to Vernon, British-Columbia and swim in lake Kalamalka, or go to Cochrane, Alberta, and go to McKay's Ice Cream Shop and take in the view and go to Cochrane Ranche and walk around in the forest to see "Grandfather Oak." It's beautiful in the Summer in Cochrane and there aren't many tourists, so you won't get sucked into crowds.