Bronx for a single family house

Check this out from 2010....
https://www.dnainfo.com/new-york/crime-safety-report/bronx/morris-heights
Bushwick and Bed-Stuy were once rated worse for safety so take what you like from that.

Also this just happened...
http://www.washingtontimes.com/news/2016/apr/27/new-york-police-arrest-about-100-suspects-during-m/
which i think shows some serious improvements underfoot

And the sales figures mean you aren't alone.
http://therealdeal.com/2016/04/27/outer-borough-bonanza-bronx-and-staten-island-home-sales-spike-35/

There is an agent in my office who speializes and live in that area. I'm sure he would be willing to talk to you about the issues:

Matthew bank
DG Neary Realty
http://streeteasy.com/profile/824406-matthew-bank

I just moved up to 176th on the concourse and have felt safe albeit appearing like an obvious gentrifier. There may also be rezoning along nearby jerome avenue that will change things even further. I decided to get in early before the prices rise. They are still some finds at pre-boom prices but not for long...The Furman center has interesting reading on gentrification: http://furmancenter.org/files/sotc/NYUFurmanCenter_SOCin2015_9JUNE2016.pdf and on housing appreciation: http://furmancenter.org/files/Q12015_9_3_A.pdf

If you can purchase a property between Jerome Avenue and the Grand Concourse, that would be ideal from an investment perspective. The broader catchment area would be between University Avenue and Webster Avenue. I would be concerned less with the particular number street and more with the specifics of the property itself: Is it a tree lined block? Is it proximate to parkland? What is the condition of the interior? Does it have original details? Does the property have violations? Does the property include parking? Etc.