Japanese think crime is pretty ridiculous in America (it's literally 100 times as bad in America) and I have had to explain to many that there is little chance of them being hurt if they were to visit, especially to younger people. Lots do visit though. They are baffled by the gun culture.
For the positive, they consider Americans very independent and outgoing. And they generally feel it's a 'cool' culture, though that's shifted a lot, as South Korea has been getting more fashionable. Obama was good for America though, especially when he was elected, he was popular here.
Those I know who've visited considered Americans very friendly, though I think it's a case of Americans being very friendly to visitors. Japanese have been very kind to me as a foreigner, more kind than I think they might to another Japanese.
As you can tell, I'm not Japanese, but I find Japanese like talking about other countries in a way that American culture might feel uncomfortable (no PC culture here, since non-Japanese is about 2% of the population, not even enough to get a petition going). So, I've heard a lot of opinions about America over the years.
