I'd highly recommend The Inn at Longmire at the base of Mount Rainier.
Good food and spectacular scenery. Hikes from easy to thouse requiring technical rock-climbing gear. You can walk out the back of the place and hike up through an old-growth cedar forest and on up above tree-line.
Mt. Rainier is accessible only from mid-May through perhaps Sept. We stayed a couple of days in May, years ago, and they had only just opened the road up to Paradise - and there was still 15 feet of snow on the ground around the Paradise parking lot.
It's a magical place for the physically fit.