Chops,
Welcome to IA. I have lived in Cedar Rapids for 15 years now.
As kevinb421 pointed out, Cedar Rapids, is divided into quadrants. I live on the SE side and we love it. The SE side has the 1 "bad" area in town (Wellington Heights neighborhood), but it is not that bad, and if you are more than a few blocks from it you won't know it is there.
Here is a brief summary I found of the quadrants:
Cedar Rapids is tilted at a 45 degree angle thanks to the river, so the city is generally divided into four quadrants (NW, NE, SW, SE). SE is the most diverse, with the wealthiest areas of the city and also the most troubled. Wellington Heights is the neighborhood directly east of downtown, and is usually considered to be the worst area in Cedar Rapids. 19th Street is the historical divider between troubled Wellington Heights and the more affluent Knollwood area. This area has a wide array of architecture, with many historic homes including the Brucemore Mansion.
The NE is the most expansive side of Cedar Rapids, generally a good bet and where the majority of apartments, shopping centers, and retail stores can be found. The suburb Marion is one of the fastest growing cities in the state. This area is home to Lindale Mall and Rockwell Collins' corporate HQ and main campus.
The NW is a small area that is generally very nice and characterized as being more secluded and hilly. Near the river and just NW of downtown is the neighborhood known as Time Check that was largely wiped out by the 2008 flood.
The SW is the industrial side of the city, with pockets of decent neighborhoods and other pockets that should be avoided. There are a number of seedy apartment complexes on the SW side. This is the other big retail side of Cedar Rapids, stretching along Edgewood Rd. It is also home to Hawkeye Downs racetrack and Kingston Stadium. Areas near the river and stretching over to I-380 were hit very hard by the flood and some still have not recovered.
This info is pretty spot on. There are nice neighborhoods in all quadrants and not a lot of things to stay away from. A few years ago I would have said CR was not a very bike friendly town, but that is changing quickly. Most of downtown and a lot of the other major streets are having dedicated bike lanes added now. There are quite a few trails for riding, and in general biking around town has gotten much better. There were massive floods in 2008, and parts of the city are still recovering. There have also been a lot of positives to come out of the flood recovery (New Bohemia neighborhood, Czech village and downtown have all seen a lot of revival efforts after the flood).
Anyway, my family and I love it here. If you have any questions or even want to meet in person we would be happy to show you around town, or just meet and greet, just PM me.