Mount Peak is the local name for Pinnacle Peak, and the Cal Magnusson Trail that gets you to the top is a very popular local hike. It's short, ranging from 25-50 minutes from the parking lot to the top. It's also easily accessible via a 5 minute drive from downtown Enumclaw, and the workout is intense. Due to the rough, steep terrain, locals often do laps on this trail to train for summit climbs up Mount Rainier.
The trail is surrounded by thick woods all the way up, and you'll have occasional views of Enumclaw and the entire plateau sprawling out below. Overhanging trees are dense enough to provide a comfortable amount of shelter on rainy days. Be warned that during wet weather the trail can be very slick, and many hikers hobble down with sprained ankles.
Interestingly, the top of Mount Peak once hosted a fire lookout, but all that remains is the foundation and two long benches that locals have erected. There is no true view at the top of Mount Peak because of the heavily wooded landscape. If you head south toward Mount Rainier and pick your way along the network of small trails, however, you will find a quaint stone bench nestled in a small clearing that provides a stunning view.
Be aware that several informal trails branch toward the top, and it is easy to become disoriented.