I recommend this trail for visitors, because you can have an easy hike to Talapus Lake, and if you still want more you can continue on to Olallie Lake. Want still more? There are a handful of other lakes reachable from this trail including Pratt Lake, which is beautiful.
Please let me know if you want to drive to this trail, and I can provide you with the required Northwest Forest Parking Pass.
Bring sturdy shoes. Poles should not be necessary.
It takes about an hour to drive to the Lake Talapus Trailhead. Follow I-90 East to Exit 45. Follow the signs to Forest Service Rd 9030.
The hike to Talapus there and back takes about 1 hour and 45 minutes. Adding on Olallie Lake adds another 2 hours.

Got a car and you're up for a long day? Mount Rainier

Mount Rainier has so many beautiful trails it's hard to choose just one. And, everyone has their favorite. I highly recommend the Skyline Loop Trail. It is a long drive and a moderately hard hike, but every time I take this trail it leaves an impression on me.
The Tolmie Peak Trail shows up on a lot of my friends' favorite trails list as well. Another advantage of this trail is that depending on the time of year, it is a shorter drive and a slightly easier trail.

Don't have a car?

Trailhead Direct bus from Memorial Day to Labor Day can take you to hikes at Mt. Si, Mt. Teneriffe, Little Si.
Take the bus to Discovery Park and you have at least two options for great urban hikes. Bus routes 24 and 33 will take you there. Use Google Maps for more information. The roughly three mile version, Discovery Park Loop trail, stays high on the bluff and overlooks the water and the mountains. The roughly five mile version, Discovery Park and Lighthouse Loop, breaks off of the loop to go down to the beach, lighthouse, water treatment plant, and bird sanctuary. Download a map to see how the trail meanders through the park. If you get lost, just ask a passerby for directions. You will not be alone in this park.