Features: Views (Olympics, Cascades, Rainier), Rolling Hills, Light Rail connections
Opened in 2007, the Chief Seattle Trail connects Beacon Hill & Rainier Valley. The entire trail runs beneath Seattle City Light power transmission lines, but despite this you will find great mountain views in every direction. The Beacon Hill & Rainier Valley ends of the trail are ~1.5 and 1 miles from their respective light rail stations.
Route
I prefer entering from the Beacon Hill end of the trail (S Angeline St a few hundred feet East of 15th Ave S) and walking towards the Rainier Valley end (S Gazelle St & 51st Ave S). Doing it in this direction means that you will be looking at Mt Rainier while you walk. For a shorter walk, you can enter/exit numerous road intersections along the trail.
Optional addons
Kubota Gardens - just over a half mile from the Rainier Valley entrance to the trail