Here is a video of the trip described below:
Just a 45 minute drive from Enumclaw (plus a five mile bike ride and a three mile hike.) Park at the Carbon River Ranger Station at Mount Rainier National Park and cycle the gradual but steady five mile grade up the old Carbon River Road, closed to vehicles but open to bikes. You will begin in the only rainforest in the park, with huge trees, moss and ferns, and of course, water. You'll even see a large snowbank near your start, unheard of at such a low elevation, but the dark forest keeps it insulated. Lock your bike at Ipsut Creek campground and head up the Wonderland Trail toward the Carbon Glacier.
The trail is generally uphill too, but not strenuous. You follow the Carbon River for most of the route, crossing it and other waterways on single log bridges. There sixteen of them, but most have a railing on one side. At about three miles, you will reach the suspension bridge. Although it rises only 30 feet above the river, much lower than the Tahoma Creek bridge at 165 feet high, it is quite long, and thus, quite lively. From its undulating center, you can gaze right into the snout of the Carbon Glacier, the lowest such perpetual ice mass in the lower 48. It is also the longest glacier (nearly six miles,) the thickest (700 feet,) and has the most volume (1/5th of a cubic mile) of any U.S. glacier outside of Alaska. If you want an even closer look, continue up the trail another 4/10ths of a mile, but don't get close to the face of it. Melting ice disgorges rocks can crush people.
If you are tired after your hike, know that going down is easy and takes about half the time. Pick up your bike, and you can coast almost all the way back to the ranger station. Driving from there back to Enumclaw is even easier.