Flight
Chicago's main airports, O"Hare and Midway can be easily accessed from the city. O'Hare is closer to wedding events however Southwest only flies in to Midway which is farther south.
House Or Rental
If you're looking to stay at an airbnb near the events, check out the following neighborhoods; Lincoln Square, Ravenswood, Lincoln Park, Andersonville, Lakeview. If your preference is to stay downtown, check out locations in the Loop.
Train
If you plan on taking the train from Kansas City, take the Southwest Chief. There are only about 8 stops and it takes about 8 hours. You will be dropped off in the middle of downtown Chicago at Union Station with plenty of public transportation options as Lyft/Uber.
Travel Note
There are not a lot of hotels close to the wedding venue. If you are looking to experience Chicago for the weekend, I would recommend staying downtown and taking a cab/Uber/Lyft to the ceremony. If you prefer to stay closer to the venue, there are a handful of hotels in the Ravenswood/Lincoln Square area. The other option as mentioned above is Airbnb.