Hobart Street Park in North Perth is a really popular one for mothers' groups during the week. It's probably for a few reasons - but the fact that it's fenced is bound to be one of them for parents of tear-away toddlers.
Shade is pretty good as well - another big plus.
Grab a coffee from the deli across the road and throw a blanket on the grass while the kids play on the swings, slides and see-saw. Perhaps pack some buckets and spades too because the playground is on nice white sand.
It's a fun play for really little kids to about six year olds. The parking is not bad provided it's not too busy. Find a spot on Hobart or Auckland Streets.