I think you're going to have to take your chances with street parking. That area is filled with UI student apartments, all looking for very few parking spaces along the street. There are very few parking lots, and any in that area will be restricted to residents and the businesses in the area.
If you are lucky enough to find a spot on a side street in that area, you will also have to worry about having it moved now and then if the streets need to be plowed while you're gone.
Your safest bet is probably to park in one of the ramps or garages in the area, but none will be free.
I would suggest calling the I.C. Parking/Transportation Office to get a better idea where to park: 319-356-5096.