Philly is a great town. I was born and raised in the suburbs of Philly, and I have a ton of family that still live in the Spring Garden area which is in center city near the art museum.
There are plenty of places in the city that are safe. The Spring Garden area is decent, and the Rittenhouse Square area is pretty nice. There are some newer areas going up down near the waterfront that I have heard are pretty nice also.
You should definitely take some time and get to know the city. In the name of self preservation, there are some really rough neighborhoods that you'd be wise to stay away from unless your packing (or even if you are packing). Just like any other big city, you have to pay more attention to your surroundings, but it is an amazing place to live.