The two most popular food options in Chicago are Italian beef and deep dish pizza. You can start arguments/fights/wars over which beef or pizza places are the best.
For Italian beef, Portillo's, Buona Beef, and Al's Beef are some of the bigger names in the city.
For deep dish pizza, there's Lou Malnati's, Giordano's, Gino's East, Uno's, Pequod's.
Tourist attractions are everywhere... The Field Museum is definitely a good place to go. The Adler Planetarium, Shedd Aquarium, Navy Pier, and Museum of Science and Industry are a few other places that immediately come to mind. Grant Park and Millennium Park are popular places to walk around and relax, unless they're closed off for an event like Lollapalooza. Willis Tower (formerly Sears Tower) and 875 N. Michigan (formerly Hancock Center) offer skydeck views of the city. Water Tower Place is a popular shopping destination.
Millennium Park has Cloud Gate, a.k.a. "The Bean". It's a silvery sculpture that attracts tons of tourists looking for photo ops. I'd call that a must-see.
From Navy Pier, you can take a boat ride out on Lake Michigan. From the Chicago River, you can get a ride on the Chicago Architecture Boat Tour. That's a relaxing, unique view of the city, and a good way to see the skyline from ground level.
If you know your schedule well enough in advance, maybe try to get tickets to a Cubs or Sox game, if baseball is your thing. For a neutral tourist with safety concerns, Wrigley Field (Cubs) is in a safer neighborhood than Guaranteed Rate Field (Sox).
Navigating the city: I assume you won't be in town with your own car. The CTA offers train and bus service throughout the city, and it's usually very reliable. Taxis are everywhere if you'd rather not deal with public transportation, and Uber is always an option, too. You could also rent a Divvy bike to ride somewhere. Walking around downtown is also feasible if you plan to stay within a few blocks of your hotel.
Safety: It's a big city. There are bad areas, mostly west and south of downtown. The main drags like Michigan Avenue are a lot safer, simply due to the number of people around, but you can assume there's always someone out looking for an easy target. If you pay attention to your surroundings and don't look too much like a tourist, you should be fine. As you noted, CCW won't be an option for you, so your wits are your best defense.