Which State/Province do you live in/come from?
My parents are from Chicago and Cicero, one of the city's suburbs. When my mother was pregnant with me, they moved to Green Bay, Wisconsin. Shortly as I was born, they moved back to the Chicagoland area, where I've lived ever since.
What makes your state special/different to others?
Illinois has a superiority complex, while Chicago has an inferiority complex.
Chicago is often called The Second City, because for nearly a century we had the second largest metropolitan population -- behind New York City. This has led to a sort of feeling that we're always playing catch-up to other cities, especially New York City and now Los Angeles. As you noted, people outside of the US traditionally only think of New York and LA, and this is, in part, because our news media often skips over the Midwest -- especially Chicago -- when it covers national stories. Examples would be the recent Black Lives Matter protests and COVID-19 coverage. Very little was said of Milwaukee, Indianapolis, Detroit, and Chicago.
That said, Illinois sees itself as an island of the Midwest, in that we are a Democrat (RE: blue) state in a sea of Republican (RE: red) states. This can give us -- especially those in Chicago -- a somewhat snobby outlook regarding the region. However, if Chicago were to ever flip red, so would the state. Southern Illinois is deeply red-leaning. And this often causes much frustration between those living in the city and those living deeper west and south in the state.
What local foods is your state known for?
Chicago-style pizza (RE: deep dish)
Chicago-style hot dogs
Dipped Italian beefs (the sandwich is 100% dunked in the beef juice)
Harold's Chicken Shack
The hero that is Tamale Guy
What special buildings do you have?
Willis Tower (née Sears Tower) was the tallest building in the world for a few decades. (Depending on when you present this information, the building name might have changed again due to it being sold.)
Wrigley Field, where The Cubs play
Soldier Field, where The Bears play
Macy's (née Marshall Field & Company) is an architectural masterpiece which people visit from around the world. They used to put up amazing displays in the windows around Christmastime, which would then draw people to The Walnut Room at the very top of the building.