A quick scan of Wikivoyage's guide to Hiroshima sights indicate that memorials and museums to the attack have English-language information. If they didn't intend non-Japanese to visit the place, they wouldn't have such information.

I seriously doubt that they'd regard the USA differently from other non-Japanese countries in this context, even though the USA was the country that dropped the bombs, or even be able to tell whether you're an American versus a Canadian or an Australian.

I remember reading once about an atomic bombing victim who is a volunteer at some museum or memorial wanting to learn English so that he could relay his experiences to English-speaking visitors.

Likewise, displays at the House of Sharing, which is dedicated to comfort women, are in English, Korean and Japanese, and Japanese people make up 40% of the visitors.

What may surprise you is that even museums at the other end of the "International Peace and Tolerance" spectrum have some support for English, and therefore expect foreigners to visit. The Yasukuni Shrine, which hosts the spirits of those who died for the Emperor in war, is criticised for including the spirits of Class A war criminals, and for its nationalist take on history. And yet, there are limited English-language explanations within the museum, and also has an English-language pamphlet. And this far-right blogger mentions foreigners visiting the shrine, including those involved in war.

Update 2016: Is it ok for Americans to visit the memorials?

YES

Photo: Shuji Kajiyama, AP

It's perfectly fine. I've been to both Hiroshima and Nagasaki in my (Japanese) high school trip including multiple sessions with hibakushas.

There is really no animosity in general. The emphasis of these museums and parks are solely on how horrible nuclear attacks and war is, and how we need to achieve world peace and eliminate all wars.

I think most Japanese would find it a good thing. Of course, you'll always be able to find people who disagree, but such views are rare IMO.

Absolutely not an issue. Just to give a first-hand perspective (though the other 2 answers both excellently cover the 'why not'), I visited the Nagasaki Atomic Bomb Museum and the Peace Park a few years back, and at no point did I feel any ill-will or awkwardness. As with any similar place as long as you are respectful you are welcome - the staff were as polite and welcoming as one would expect of a Japanese visitor centre or attraction.

It's a sobering experience, but one well worth doing regardless of nationality.

As far as I see it, it won't hurt any Japanese citizen's feelings if you visit the Hiroshima & Nagasaki memorials. It rather depicts some sign of empathy towards the victims (unless you end up doing some random foolish act at a place of such deep meaning for the natives).

First off, you as an individual, are not accountable for a decision made by your country's then president some 70 years ago. Of course, it was a bitter experience for the natives but I don't suppose they would feel culturally hurt for it.

For an analogy, as an Indian, I don't hold every tourist from the UK accountable for say, the Jallianwala bagh massacre. Or rather, would you feel culturally hurt, if some Japanese visits the Pearl Harbour memorial, or for that matter, a middle-eastern the WTC memorial? Hopefully not.