Need apartment/house hunting help for moving to Michigan!!!?

I currently live in a suburb of Chicago w/ my hubby. My husband is up for a promotion with his company but we would need to move to the Lansing, Michigan area. I went to college there ( Michigan State ) so I am familiar with the area, but it has been about 10 years! We need some solid advice on looking for an apt or small house to rent.

We want 1-2 bedrooms, and really have only 3 necessities - must allow a cat, be a safe neighborhood/building/area, and have a Washer/Dryer in the unit.

Our budget is $1000/month or less. All help is appreciated...thanks!!!