Here is a thread to help you out. I am in Seattle business and was able to check out a few tennis facilities:
* City of Seattle - Amy Yee TC: not much action and was in the ghetto. Outdoor courts were closed to resurfacing, and they have about 4 indoor courts.
* Robinswood had some 3.0-3.5 league going on the 4 outdoor courts, and the 4 indoor courts had a big group beginner lesson.
* Green Lake Park courts was nice, 4 courts right on the water, no lights though. Some 3.5 action.
* Upper Woodland Park courts is right around the corner from Green Lake, 4 courts no lights, some 3.0 action.
* Lower Woodland Park courts are your best bet. 8 courts 2x2 all lit late, with lots of 4.0 - 5.0 players. These courts are between the Upper Woodland park courts and the Green Lake courts right next to the gigantic soccer field. . .
Good luck and hope this helps . . .