I'd definitely suggest the Lake Quinault Lodge: it's history, ambience, and location is really convenient for seeing much of what Olympic Park has to offer. It is on the southern end of the park; the Hoh Rain Forest is nearby as is the coast.

We stayed there two years ago and are returning this fall for an extended stay. We liked the accommodations; delicious food; history of the lodge; and the general ambience. It's located on a beautiful lake; hiking trails right there and if I remember correctly, canoes for use on the lake. The grounds are spacious, perfect for kids playing while parents relax.