Most pilots choose to camp at Beebe Campground on the Colombia River. Beebe is an awesome facility with pristine grass, clean bathrooms and nice camp sites. Sites are $25/night and are first come first serve. YOU CANNOT RESERVE SITES. There is a max of 8 people and 3 vehicles per site.
In order to get a site on the weekend during the summer you usually have to be waiting for someone to leave around mid-morning and grab the site immediately it becomes vacant. Sites are much easier to come by mid-week. Beebe Campground is located 10 minutes drive from Chelan and 5 minutes from Chelan Falls Park.
There is also the Lakeshore RV Park located near downtown Chelan. While the Lakeshore RV park has a more central location within walking distance to Restaurants and shops it is not as nice, more expensive - but it does take advance reservations.
Chelan is a resort town located 3 hours from Seattle. There are a number of centrally located motel options. Here are some links to a handful of good hotel / motel options.