The entrance to Wallingford Playground can be found opposite the main entrance to Waitrose car park, here.
There's loads of parking in Wallingford. It is all well signposted.
It was quite a muddy day so we didn't stay long. However, we'll go back:)
Obligatory toilet info:
Wonkey camera work...
There are actually two play areas.
Smaller playground for little children:
Very fast merry-go-round.
And the park for older children:
Free app, here.