Are there any famous or distinctly 'Chicago' restaurants in the city?

All the above are great suggestions. When I have people visit from out of town I like to take them to THE CHICAGO PIZZA AND OVEN GRINDER COMPANY, or The Green Mill. Both are entrenched in Chicago History as having connection to some of the most famous Chicago Gangsters including Al Capone.

As others have mentioned, there are probably too many to list, so a good place to start is with what kind of restaurant you prefer. If you want someplace super-casual, you might be interested in the Billy Goat Tavern or Hot Doug's. If you want upscale Italian, there's Spiaggia, for instance, which has long been considered one of the finest Italian restaurants in the U.S. For something more unique, try Alinea or (if you can get tickets) Next.

So much depends on your preferences and tastes, so a good place to start is a site like Yumbly.com that lets you search by exactly what you like to eat, and then of course Yelp for lots more reviews by other diners.

My favorite "distinctly Chicago" restaurants: The Berghoff and Italian Village (Loop), Gibson's and The Pump Room (Gold Coast), Manny's (South Loop), Erie Street Cafe and Green Door Tavern (River North), Twin Anchors (Old Town/Lincoln Park), Arun's (Albany Park), Sabatino's (Irving Park), Ann Sather's (Lakeview), and Small Bar (Logan Square).

There are a ton of great places to eat in Chicago! Actually, too many to name, but one place I always suggest folks check out is The Parthenon. It's in Greek Town and not too far from The Loop. The food is incredible. Check it out for sure, and try the Saganaki.