For an enjoyable one-mile walk on a winding trail through the forest and around the creatively named First Lake and Second Lake, look for the Two Lakes Trail behind Alaska Vocational Tech Center (2nd Ave. and C St.). There’s a picnic area at the trailhead.
The high bare slope hanging over Seward [1] is Mt. Marathon, featured attraction for the 4th of July Mountain Marathon Race [2]. It generally takes nonrunners at least four hours to get up and back. Follow Jefferson Street due west up Lowell Canyon and look for the trailhead to the right just beyond a pair of large water tanks. You can run all the way back down the mountain on a steep gravel incline if your legs and nerves are good, but beware of slipping on the solid rock face near the bottom.
The trail does not actually reach the summit of Mt. Marathon (4,560 feet) but rather the broad east shoulder (3,022 feet), which offers a spectacular view of Seward and the entire surrounding country.
Links:
[1] http://www.moon.com/destinations/alaska/kenai-peninsula/seward
[2] http://www.moon.com/destinations/alaska/kenai-peninsula/seward/entertainment-and-events