The best option, time-wise, is to fly directly into Champaign-Urbana University of Illinois-Willard Airport (CMI). It is serviced by United Airlines via Chicago O'hare International Airport (ORD). American Airlines also services Champaign via Chicago as well as Dallas/Fort Worth International Airport (DFW). If flying into Champaign-Urbana, take a cab to your desired destination.
Midway Airport also services Chicago and offers other airline options that may be less pricey. Bloomington, Illinois, airport is a one hour drive from C-U. Indianapolis is a two hour drive if you would like to look into more airline options.
If flying into Chicago O'hare International, you have three options:
(1) Amtrak Train Union Station: A direct one hour subway ride form O'hare. Or a shorter cab ride. It takes 2-3 hours to the Illinois Terminal in Champaign. Buy your ticket ahead of time to save on the cost. Arrive at least 15 minutes before the train departs. Once at the Illinois Terminal in Champaign, a local bus can drop you close to IYCU (MTD link) or pay for a $5 cab ride.
(2) Book a charter bus with Illini Shuttle or Peoria Charter Coach Company. Most routes can take 3-4 hours and have several drop off points in Champaign-Urbana. The closest stop to IYCU is Illinois Street Residence Hall or "ISR". It is on campus and is an easy 15 minute walk to IYCU.
(3) Rent a car. Easily available at O'hare at baggage claim where a bus picks you up to take you to your preferred rental car service. You take the tollway south to where it connects to I-57 which goes directly to Champaign-Urbana by going East on I-74.