However, I cannot find a single public basketball court in either neighborhood you mentioned, and I can see maybe one park per neighborhood that can each support 1 open space sports game which means my friends and I would have likely had no opportunity to find an open space to play a sport game when growing up due to how crowded parks are.
Add on the homeless problem here and it should come as no surprise my GF and I are planning on moving back to my midwest hometown once we start trying to have kids.
There's Gilman Playground in Ballard with baseball park. It also has tennis courts. There's another baseball park at NW 63rd St and 20th Ave NW, and another one at 60th and 26th. There are more baseball parks in Woodland Park, and they also have soccer fields. Ballard High School has a football stadium, though I don't know how easily accessible it is to non-students. There's another baseball park/football/soccer stadium at Local Heights Playfield.
But yeah, if you're into basketball, you're probably out of luck if you're looking for any outside basketball place, it's not really that popular here.