The Madrona Playground in the Madrona neighborhood is a gem. It's a new-ish park, and there are some fun toys to play on/bring your children to play on.
Location: 33rd Ave & E Marion St
Number of swings: 2 regular, and another set with 1 baby swing and some hanging chains that once were attached to a swing of some kind.
Ground material: Wood chips
Chain length: Medium.
The chains were medium-long, I'd say, but they were thicker than what I usually find in Seattle.
I was impressed by this park. It was full of people attending some sort of bbq when I came through, but getting a spot on the swings wasn't a problem. The chain length was such that I could get some good momentum.
How to get there: Bus routes #3 and 84 stop at 34th St. in both directions.