RE: Philadelphia/Center City
Reading Terminal Market would have to be a must-visit. The Pennsylvania Dutch place always has a line. Jim's Steaks are the real deal. Delilah's, in the Market, always gets good reviews.
And just walking around looking at the shops -- meat, seafood, produce -- is a food experience.
And the Market has one of the best foodie bookshops I've ever visited. Never leave without a volume or two.