If you're used to having a dog in an apartment then it's not hugely different just a lot less grass, especially in that area. Rittenhouse park might be your nearest patch of grass, lots of people take their dog there. Only other advice is to take advantage of the city, go places and do things, you'll be in prime downtown area for events, not to mention some of the best restaurants you'll ever see.

Philly is hard to pin down aside from the bigger areas mentioned above and everyone has their own threshold. Find places you like and once narrowed down do a dry run of regular things like a grocery trip, trip to work, train, park etc and look around. Make sure it meets your safety standards.