Bonnie
Well, it depends on if you want indoor or outdoor. Is it a summer birthday?
My son has a summer birthday and one year we rented one of the shelters at Linclon Park (#5 by the wading pool). It rained that day! Then another year we had his birthday at Coleman Pool. (awesome weather, luckily) I’ve been to parties at Camp Long and that was a lot of fun.
For indoor you can rent rooms at all the community centers. The Little Artist does a nice birthday party. I’ve been to parties at West Seattle Bowl. (fun party but SUPER BUSY) Might be pricey but you can rent the bathhouse for a party down on Alki.
Of course, the Y has great birthday parties. We’ve been to a few there too. You can also do swimming parties at the Y and Southwest Pool (when they reopen)