The best news is the trail through Riverfront Park  and the new Union Street Railroad Bicycle and Pedestrian Bridge over the Willamette River (previously hard to cross without a car). The bridge links Riverfront Park with Wallace Marine Park on the west side of the river.
Another good place to cycle, skate, or walk is Minto-Brown Island Park (2200 Minto Island Rd. SE), a large natural park with lots of trails and an off-leash dog park. Find it along the east bank of the Willamette River south of the capitol area.
The Salem Golf Club (2025 Golf Course Rd., 503/363-6652) is one of the best public courses in the state. Another option is Santiam Golf Course (8724 Golf Club Rd., Aumsville, 503/769-3485): If you drive 15 minutes east on Route 22 (at Exit 12), you can look forward to combining a round of golf with a walk in the country. Low greens fees and a full-service restaurant and bar add to the pleasure.