Consider working with a professional like a licensed Real Estate agent, also you can drive by these neighborhoods in the day and I suggest at night too! Do some research if your going to a totally new neighborhood. As with my clients I will personally take them around the neighborhoods and we will tour local shops and schools.
Our office has an extensive rental department you can call our main number at 347-202-4965.
Best of Luck!
Exit Realty Search
3928 E. Tremont Avenue
Bronx, NY 10465
When you are considering moving to a new area you should contact a local Realtor and drive the neighborhood to view some properties.
As far as the crime rate you can do your due diligence online or by contacting the local community board in for that area.
Morris Park Realty
As for transportation--see link since no area is given-- http://www.hopstop.com/