I'm not able to give any Seattle specific tips for locating salmonberries, as I'm a bit further north. However, as a starting place I'd recommend forested trail systems, especially those with water, sometime April through June. They do better in wet and partially shady environments, rather than the dryer brighter areas next to roads or bike paths where you find blackberries. The disturbed areas near edge of a forest is also pretty good place to look for thimbleberries, which ripen later in the season (June-July). They aren't as juicy or sweet as blackberries, and I don't think I'd take a trip for them, but I'll usually pick a few if I spot them.
I'm not able to give any Seattle specific tips for locating salmonberries, as I'm a bit further north. However, as a starting place I'd recommend forested trail systems, especially those with water, sometime April through June. They do better in wet and partially shady environments, rather than the dryer brighter areas next to roads or bike paths where you find blackberries.
The disturbed areas near edge of a forest is also pretty good place to look for thimbleberries, which ripen later in the season (June-July). They aren't as juicy or sweet as blackberries, and I don't think I'd take a trip for them, but I'll usually pick a few if I spot them.