Iowa City is a bit different in that there are management companies that rent out most of the apartments. The nice thing is that you can contact one company and see what they have available, or go look at all the properties a particular company has on the market. If you can come into town for even 1 day, you can make appointments with a few companies and see a ton of apartments. Here's one company http://www.apartmentsiniowacity.com/
but there are a few other good ones (I recommend Heritage Property Management as well) if you Google "Iowa City apartments" or something similar.
The nice thing is that you might be able to find a 1- or 2-bedroom near the law school (that basically means on the west side of the river) for a low enough price that you don't need a roommate. I have a 2-bedroom by myself, and I use one room as an office. I know people who had a lot of luck using the official roommate list as well, but Craigslist just hasn't caught on enough here to be a very useful resource for housing--especially since the management companies do most of the letting rather than individuals. If anyone is looking for some insight on a particular area or apartment complex, please feel free to ask me.