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... was going to southern Italy.
I've never been anywhere where there were more people out to find a way to cheat me. Don't get me wrong. I feel very lucky to have gotten to visit some of the most impressive ancient sites around. My wife and I got to see the Colliseum, the Forum, the Pantheon... We made it out to Pompei, which was incredible, and we even spent a day on the beautiful island of Capri. But seriously, nearly every person with whom we interacted in a situation where there was money involved attempted to cheat us. The bread-on-the-table trick was extremely common, though luckily my wife had been before and was ready for it. We also got ticketed on a train ride we thought we had paid for. At the famous Blue Grotto, they charged us one amount but afterwards gave us the ticket stub that showed they were supposed to charge half that.
I believe though that this is not generally the case everywhere in Europe. I've also traveled to England, France, Switzerland, Germany, Spain, the Netherlands, Belgium, and even elsewhere in Italy and in general I've not felt like I constantly had to be wary of scams. Prices may be high right now due to the exchange rate, but at least you know what you're paying in advance.
As for the anti-American sentiment... I don't think it's really pre-ordained. If you fit the stereotype of the fat, loud, ignorant American, then I supposed you might get treated as such. I mean, I once saw an American tourist get shocked when the French restaurant wouldn't take US dollars. Show some awareness of where you are. And learn some basic phrases in the language of the place you're visiting. It's amazing what just a little cultural respect will do. (Except in Paris, where they seem to detest you more if you butcher the language than if you can't speak it at all.)
In general, as long as you try to keep in mind what you expect of visitors in your own country, you'll do fine visiting someone else's.