Unless you are in a hurry to get out of apartments, I'd rent on the north side to be close to work. In Cedar Rapids, that means addresses on the NE side and possibly some SE, Marion or Hiawatha (I can't think of many apartments in Robins, but I could be out of the loop!) You'd also be close to Lindale mall and the Collins road restaurants and grocery store. Get your feet under you for a year and explore the place and then move to a different type of housing/different area if you decide that's what you want.
There are loads of places to rent, many newer. I can't believe Collins isn't providing you with more information! I mean, it seems like the HR department is as big as some small countries... I know the CR Chamber has provided information before when I was trying to recruit people from out of town. Try them
The Cedar Rapids Area Chamber of Commerce -- down at the bottom, email to ask for one of their relocation packages and explain your situation and ask if there is anyone else you should contact.