Speaking of which, I'm bringing on a rental place in bellevue this week. What kind of place are you looking for?
I agree with James on his comments. You will want to start looking at least 30 days before you move. I recommend actually shopping around before that if it is not too late for you. I would start looking 45 days out to make sure I have enough time to find a good home with a decent rental. If you wait to late you may feel pressured to take whatever you can find and then have to pay more because you had to take something right away.
I hope this information has helped in some way.
I agree that Craigslist is a great place to start.