Our endless number of great BYO's are unique. These are generally small chef run places where a great amount of love and attention is put into the food. Bibou, Melograno, Kanela, Cochon, Lolita etc, etc,
It is hard to say that one thing is representative of the food culture here. I happen to love our variety of ethnic food.
There's a few different ways you can go with this:
1. Classic cheeseteak route. Although there's much debate on the merit of these sandwiches, you can't deny the sheer spectacle that is the Pat's/Geno's rivalry at on 9th st in South Philly. I recommend walking south to enjoy the Italian Market (buying beautiful Italian goods at Dibruno Bros, then wondering at the live chickens in the Little Mexico section), and ending up at the bright lights and long lines at either of these two institutions. My favorite is served at John's Roast Pork, but they usually run out of food by 1:00 PM.
2. Beer city route. We have amazing beers here. And we were one of the only places 10 years ago to get the best Belgian Imports. If you don't mind the crowd, you must go to Monk's. The beer is a little overpriced and the host can be surly, but the food is tasty, and I'll eat my hat if you have a bad time.
3. Restauranteur Route. Steven Starr and Jose Garces have turned this town into one of the best eateries in the country. I vote Garces, but Starr has done some great work too. Continental was one of the first places that kicked off the restaurant renaissance. Check their sites.
4. Northeast Slavic route. Ok, so apparently there are these restaurants in the Northeast part of the city (you'll need a car) that charge like 75$ or $100 a person, and include every kind of borscht and goulash you could ever eat. Oh, and the vodka - I can't forget the vodka! I've read stories of dancing on tables in the wee hours of the night. My goal in life is to go to one of these places and live to tell about it.