Hi PIMO,
We've been going to Plakias for a while now, since our now 13 year old was about 8. I asked her, and she said "The beach and the pool", so I think that answers your question. I'm trying to think if any of the tavernas have a playground, but nothing springs to mind.
Perhaps I'm just not observant, so hopefully someone will prove me wrong.
Enjoy Plakias with or without playgrounds.
I've returned to edit this with a word of caution - safety - some playgrounds appear to be lethal compared to the standards that apply in the UK, despite us all being covered by the same EU legislation - one example is a helter-skelter which had no level bit at the bottom and meant an 18 inch drop onto concrete at speed. If you have a three year old I am sure you are constantly scanning for dangerous items anyway, and I'm not telling you anything you don't already know!
Arnaki