Hey WSBRIT: Not sure if your kidlet is mobile yet but you will definitely want to check out Ercolini Park (corner of Alaska and 48th Ave. SW) — it’s the best little park to get the little ones started IMO. You might also want to pick-up the Free kid magazines Seattle’s Child and ParentMap — both include calendars of things happening around the city both 1-time activities and ongoing ones. They are often in the paper boxes (at least at Westwood post office) or in grocery stores.
The Sandbox in Georgetown is pretty cool (although your little one might not be old enough or ready yet).
The local community centers have “open gym” times at most locations. Red Tricycle is a great resource as is “Things to do with Kids in Seattle” FB page.
WELCOME!!