Visit this:
http://www.visitphilly.com/philadelphia-neighborhoods/
There are safe areas everywhere, but, these are the ones I know well:
Center City is safe. I used to live nearby at an apt at 12th and Locust (not my apartment, but staying with buddy and his wife). It is an area with a lot of LGBT support (rainbows on street signs). Very safe.
Fairmount is safe, just don't venture far over Girard. By zoo.
Rittenhouse is safe.
If you keep going west you get into the burbs which are safe, Manayunk, etc.
The east side of west philly close to UPENN / University city is safe
The upcoming parts of Northern Liberties are safe
Old City is safe
South of South is safe for a good while (that means South of South Street, which is a hip area)
Areas around Jefferson Med School are safe
Temple area is not safe
North Philly has a lot of unsafe areas
West Philly can be unsafe
South Philly is pretty safe depending on the neighborhood and being south of Oregon seems pretty good overall (near stadiums).
This is all I can speak to as those are the parts of Philly I know well / have lived there myself / have friends that live there.
Course, it is a city, so, could get mugged anywhere.