Depending on where you are in the city, there are a couple options for off-leash dog parks. Before you take your dog to the dog parks in Philly, you should scope out the park to see what kinds of dogs go there and if you think it's a safe spot for your dog. If there tends to be a lot of large, dogs at the dog park in the evenings and you have a small dog, maybe try to go earlier in the day. Since there are only a few dog parks in the city, they tend to fill up often and you can't be sure that all dogs are friendly, well-trained or responsive to their owners.
In my opinion, the two best dog parks in the city are the Schuylkill River Dog Park and Triangle Dog Park. Schuylkill River Dog Park has a small dog section and a large dog section, which is really nice. Triangle Dog Park is in Fishtown, and rarely has a ton of dogs there. Orianna Dog Park is also nice, but this park is a membership only park. There is also a small dog park in Passyunk Square.