Taipei is full of really great parks. The equivalent of central parks would be Da'An park which is under construction at the minute (6/2020-???)
So we're exploring all the other parks that we find the kids could play for a long while in the city.
The park that we went to is right by the Toy bank, which is near Shandao temple station on the blue line. It is also right next to Huashan 1914 creative park which is more like an art center of sort and the children's park is the one that we spent some time at as it has slides and sandpits and a train tunnel. There's also some zip lines that if your kids are brave enough to go on is very fun also.
We were there in the summer and then our son's class was also there so it can take a lot of kids.
Be sure to bring your own sand toys, hats and sunblock, and bug repellent if appropriate.