Discovery Park is a popular place to go for a walk on a nice sunny day. While there are numerous trails, the Loop Trail provides an enjoyable and relatively easy 2.8 mile journey through the park. The park has directional signs at most intersections so it's pretty easy to find the Loop Trail from wherever you enter the park. And, being a loop, you can go clockwise or counter-clockwise, depending on your preference.
Along the way, you'll cross other trails that can take you on side trips, such as down to the water. However, the Loop Trail itself offers some good views. Most of the trail is forested with moderate changes in elevation. There are many trees and logs and in the winter months you'll see plenty of moss.
Aside from crossing a couple roads, some of which are no longer used by vehicles, there's not much to interrupt the beautiful northwest forest. If you're walking counter-clockwise, you'll eventually cross a street and pass by a military housing development that is part of Fort Lawton. After ascending a hill, you'll see a beautiful view of the Olympic Mountains and Puget Sound.