There aren't a lot of neighborhood places that do deep dish, at least on the north side of the city (or maybe we Chicagoans just ignore them
). I'm not as familiar with the south. Pequod's is one, plus there are the Gino's, Giordano's, and Malnati's around. For what you want, your safe bet is probably Malnati's or Gino's.
Art of Pizza is good, but more of a takeout joint with a few tables.
I haven't been to Bartoli's in Roscoe Village but have heard people say it's good. Supposed to be similar to Gino's, on Addison and Damen, nice little neighborhood. I won't personally recommend a place I haven't tried though.