Vetri, Sansom Street Oyster House, Little Fish, Osteria, Fountain, Dim sum at Joy Tsin Lau, forget the naysayers, there's more to cheesesteaks than cheese and steak, going to Pat's and/or Geno's is as much for the experience as the steak, Monk's, Belgian Cafe, Slainte, Amada, Le Bar Lyonnais, Le Bec fin, La Croix, Buddakan, Morimoto, Gilmore's, (and my neighborhood options: Sycamore, Bona Cucina, Marigold, White Dog)
These are my absolute top picks. the fabled list of the top restaurants that I would be happy with for the rest of my life if forced to choose.
Of this list, if you can at all swing it Vetri and Little Fish are simply awesome experiences. Only problem is that it takes months to get in either. I have a monthly reservation at both but neither one is until late in September.
For hanging out and not necessarily eating: If you are young and out and about at night: South street. More sedate: Old City. Art museum area is a must on a nice afternoon. Chinatown is great for weekend brunch - Joy Tsin Lau. Riverside is great during Philly Beer Week. Actually the whole city is great during Philly Beer Week.
Best Beer in town: my house of course