That's a pretty tight budget. There are basically two areas that I am going to recommend for you. First is "Southwest Center City", which is going to be the best bet. The area I would look in is bordered by Washington Avenue on the north, Broad Street on the east, I76 to the west, and Passyunk Ave to the south. It's not a great neighborhood but it is a neighborhood that is very centrally located, safer than north Philly. The neighborhoods in that section are Newbold, Point Breeze, and Grey's Ferry. You should be able to find something in your price range, and if you are lucky you could do it within 10 blocks of the Broad Street Line. Beware, parts of this area are rapidly gentrifying.
The second area I would look in is Brewerytown/Strawberry Mansion. This neighborhood is right on the edge of a gentrifying area and I think it's going to be one of the areas that will see sweeping changes. That said, the housing stock in Strawberry Mansion is some of the best I've seen in the city. Really great old victorian homes, but all of them need a lot of work. Strawberry Mansion is right on Fairmount Park.
Neither of those areas are close to rail lines, but a word of advice about Philly compared to NYC. Buses are the primary mode of mass transit. Buses run EVERYWHERE. You may not be able to get a train, but you'll be able to get buses wherever you need to go, and they operate on a frequent schedule. Since Philly is a grid like NYC most times you'll only need to take two buses to get to your destination.
