Since the OP asked about "cheap" lodging, none of the B&B's and downtown North Creek lodgings apply. Here is the list of cheapest (or most affordable) lodgings in order and unbiased:
Northwind Motel
Inn on Gore
ValHaus
Black Mountain
All located within 5 minutes of Gore. Even if you can find less expensive out of town you'd probably make up the savings in increased fuel costs.
For someone who wants nice, the Alpine has the nicest motel rooms in town. Try one of the guys who support this blog with their ads if you want to rent a house or condo.
I Think, Therefore I Ski