You can take the train (SEPTA) from the airport to downtown it is only 8 miles. You get a view of different parts of the city and can check out downtown PHL. More and more cities you can do this.
I agree about taking the train into the city. Head for Society Hill and Penn's Landing along the river. If you stop in at the Sheraton or the Hyatt, I'm sure the concierge can give you lots of useful information.
Take the R1 line from the airport to 30th St station. switch to the Market-Frankfort line and get off at 2nd St.