I am looking for an area with young professionals (age 21-28). What areas should I look into?

The best nightlife means you will want to stay close to Center City, but that will mean it will be very overpriced and difficult to park your car.
There are also many neighborhoods that allow easy access to Center City. South Philly is probably your best choice for being close to Center City and public transportation without paying too much. Depending on which parts of South Philly you decide on, however, parking can be an issue.
Anywhere around Passyunk Square is difficult to park but has lots of nightlife, bars, restaurants. Pennsport or Whitman will allow easy access to 76 for driving, or many bus routes to Center City. Whitman is very quiet because there are a lot of families and professionals, but has lots of bars concentrated on Oregon Ave if you do choose to stay in the neighborhood. The prices are reasonable, and the neighborhoods are relatively safer than other parts of the city. Fishtown is a little out of the way but has a good amount of nightlife there on its own.