These numbers may be outdated, so call ahead to confirm.
The first is the
Airport Shuttle Service (1-800-725-8460). They charge $28 (one way) and $51 (round trip). They are located within the airport and while it is recommended that you make a reservation ahead of time, you can also get a shuttle after you arrive at Cedar Rapids.
The second is
Airport Express (1-800-383-2219). They charge $26 (one way) and $47 (round trip). They are not located within the airport so you will have to make reservations ahead of time.
There are also taxis that will take you from the airport to Iowa City. They generally charge about $45 (one way). I'm told if you call in advance, you can get better rates see
http://www.number1cab.com/ - $30 one way (I'm told)
Renting is another fine option:
http://www.eiairport.org/at-the-airport/transportation/