For our local specialty of deep-dish pizza, Lou Malnati's is still the best. They have several locations in the downtown area, including State and Rush, Michigan Ave and Hubbard (at the river), and Wells and Hubbard. They get very busy, but you can phone ahead with your pizza order and I think this gets you seated when it's ready. I think.
For Mexican, go to Rick Bayless's famous restaurants. Frontera Grill is the main, moderately priced one. Topolobampo is the upscale one (but moderately priced for lunch). If you're seated at the bar at Frontera, you can order items from either menu. He also has a sandwich place next door called Xoco. And his Tortas Frontera outlets at O'Hare have the best food at that airport.
For Italian, I agree with the previous recommendation for Quartino, which is sort of a small plates Italian format. (Eataly's concept is a gigantic combination of a mall and a food court, everything Italian.)
For Chicago hot dogs, Portillo's location on Ontario is convenient.
You didn't mention seafood, but GT Fish & Oyster has incredibly fresh fish and is one of my favorite places downtown.
Another outstanding place that doesn't fit into any category you mentioned is the Purple Pig, whose menu features everything from seafood to charcuterie to organ meats. They were always mobbed pre-pandemic with 2+ hour waits but I don't know how true that still is.