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By Car: Iowa City is located at the intersection of Interstate 80 (east-west) and Interstate 380 (north-south). If you have a map, it's no problem to get to Iowa City by car.
By Air: Iowa City has an airport, but it is used primarily for private and charter planes. The Cedar Rapids airport is about 20 minutes north of Iowa City. This is the most convenient airport to fly into, but airfares are often farily expensive. Moline, Illinois is 1 hour east of Iowa City, has an airport, and often has substantially cheaper airfares than Cedar Rapids. Des Moines is 2 hours to the west of Iowa City, has a wider assortment of flights, but is usually the most expensive of the three airports. If you don't mind driving, you can also fly into Chicago, Minneapolis or St. Louis (each about 5 hour drive from Iowa City).
In any case, you will probably want to rent a car after you arrive. There are taxis/shuttles you can take from Cedar Rapids into Iowa City, but having a car will definitely help you get around. There is city and university bus service in Iowa City, but limited public transportation options outside the main areas.