If you use common sense and treat the people around you with respect, you are setting yourself up to be ok in any neighborhood.
Don't fool yourself that buying cheap in a rough neighborhood is a guaranteed road to riches though. The people in your neighborhood may not appreciate your activities or presence. There are stories of rehabbers being targeted for beatings or worse...not likely but possible. NY, like Philly, is experiencing an uptick in violent crime that may slow down or even reverse the ongoing gentrification of the city...and some neighborhoods may never appreciate for various reasons. I'm not saying I think this is likely, but it is possible. People with means can always leave the city. Just because the most recent trend is that people with choices are choosing to try to stay doesn't mean that trend will continue over the long haul you are talking about.
I am already hearing stories about my friends and neighbors who started their families in New York City -- especially Brooklyn -- and sent the kids to the public elementary schools, but are looking to cash out and move to the suburbs because of the lack of decent public junior high schools. They just can't see adding private junior high and high school bills to the already very high cost of living. This might be the greatest threat to the ongoing gentrification of the borough.
That being said, buy something close to a subway stop and I think you have a strong chance of seeing it appreciate over time, and have a good time and meet interesting people while doing it. Good luck!
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