For most people I know, myself included, if someone says, "Oh you poor thing, bless your heart." in response to something someone says, it is genuine. It's only when it goes with a comment made by the person saying it that's it's an insult. For example, "Bless her heart, she's just not very bright."
BTW, I visited NYC for a few hours one night. I found most people to be very polite, especially the police officers. I did notice that people were less apt to start conversations with people they don't know. In my area, people will strike up a conversation with anyone.
Also, in most areas of the south, people accept outsiders pretty well. In my experience it's only in the small tight knit communities that people are shunned.