What a fantastic hike! Beautiful scenery, plus a break from the crowds--this hike is really for those who are in good physical condition.
The first three or four miles are easy, a slight gradual rise along the Westside Road (currently closed to traffic, due to the road being too badly damaged from floods). There's a nice view of the mountain from an old, no-longer used campsite about two miles in. It's easy to miss off to the right of the first 180 degree switchback.
Once you hit the Lake George trail, the hike increases in difficulty but is well worth the effort. As you head uphill towards Lake George, you'll catch glimpses of the Tahoma glacier through the trees--it feels as if one could reach right out and touch the snow. At the lake, enjoy the serenity. The sun (on a nice day) brightens the lake, which is a nice contrast to the thick forested trail. There are several camp sites, as well as a shelter. A trail meanders around the right-hand side, with more awesome views of Mt. Rainier.
From Lake George, the trail rises to Gobbler's Knob. Although very steep, it's only about 1.5 miles or so. The view is almost non-existent on the hike up. But, you'll suddenly break through the forest to the fire lookout, and be rewarded with an amazing 360 degree view. To the east, Mt. Rainier looms. On a clear day, you'll also be able to see Mt. Adams, Mt. St. Helen, and Mt. Hood, and even the Olympics.
On your hike out, be sure to visit the Marine Memorial, on the east side of the west side road, just up a ways from the Lake George trailhead. This memorial is dedicated to the 32 Marines killed in a plane crash on the South Tahoma glacier in 1946. Silent - mysterious - awe-inspiring.