@Immajean: I mostly agree w/ColorlessGreen. Avoid Lucas, Dodge, Governer, College, Market, Gilbert (basically everything a few streets north and south of burlington from the river to the edge of town). A little North of town on the East side tends to be more residential house-like (Brown St. historic district). West of the river is the medical/dental campus...it is quieter but you'll tend to find more massive apartment complexes than affordable houses.
If you REALLY want an affordable house, or 2 bedroom apartment try Coralville (CHEAP! BIG!). There's a decent Coralville bus system that gets to campus (I know at least 2 grad students who do this daily). There are also a few commuter lots where you can park and bus (the cambus is free, and it's a discounted rate for parking). It's absolutely ridiculous to park on campus. So if you want to be in biking/walking distance stick with the West side and the Northeast parts. Otherwise, driving from Coralville will be no longer than 15 min.
@lo22 START LOOKING NOW. For whatever reason, it's an incredibly tight rental market. If you want to be at all close to campus in a decent place, check craigslist ASAP.