If you want to stay near the airport and have easy access to public transit, look for a hotel which runs a free shuttle to/from the airport. You would have great access to public transit by taking the Airport Line to Center City. Alternatively, you can stay in Center City and all major chains have properties walking distance to Suburban Station (where you can catch the train to/from the airport). This means you won't need to worry about the frequency of trains to/from the airport to go into town and can just take the train to/from the airport for your flights (probably what I would do imho).

As for cheesesteaks, definitely a fan of Jim's Steaks. Great steaks and not touristy. You will also find many threads with a quick search full of recommendations. "Center City Restaurants" as a search phrase should yield some good results.