I lived in a nice neighborhood in London and a not so nice one. There was certainly a difference.
My good friend lives just outside of Detroit, and it's a pretty decent area, however, in the city center itself is not so good. This can usually be said about Oakland, DC, and Boston, too where inner city crime is pretty bad and very hard to avoid. I had a friend who taught in Oakland and he noted the incredible violence from end to end, including unfortunately once safe areas in the hills. My best friend lived in Boston most of his life, moved out to California, and when he went back to Boston, he couldn't find one good area anymore and areas of his youth once safe were no longer there. DC, I will get to that later.
Some cities, also noted for crime (remember this is America where guns are legal), there are cities with entire good sections in the city center and bad sections like New York, San Francisco, and Los Angeles and there is "some" distance between good and bad neighborhoods. Your safety in those cities, not unlike London, is greatly increased than the earlier cities mentioned.
And then there are major American cities with unusually low levels of violent crime like San Jose. That being said, it's still an urban city and there is crime/gangs you won't find in a nearby outlying area like nearby Mountain View or Woodside. If I had to live in the city limits of a major American City, San Jose would frighten me the least.
While Detriot, DC, Oakland and Boston are in my opinion places I would never live if anywhere near downtown/city limits, you may want to search for a good real estate deal in a US city where it's not infested with crime. Of course, these areas are known and that explains the higher prices you will find in a nicer NYC, San Francisco, or Los Angeles neighborhood, being just far enough away from a really bad area. The first cities I noted do not generally have large enough isolated pockets of safety and are ones I would avoid at all costs.
My brother just moved out of one of those terrible cities, DC, and moved from the city center quite a bit a ways out in a safe neighborhood in Virginia. Big difference. While there may be a good block in the first cities, there is that chance you can get attacked or worse with a short walk from there and in too many cases, the violent crime comes to you.
In the end, if low price and home ownership in the US is what you really desire, better off with a suburban or rural property and unless you have been in a large American city, stay away from the more notorious ones. Don't just do Google searches on crime rates, but be in correspondence with people who currently live in those major American cities to get a realistic picture. I get my picture from having lived in the city, or know families and friends from every city I mentioned. In no way am I saying the people of one city are superior than the people of another city, but violent crime is a reality in some major cities more than others.