Jells Park is in Wheelers Hill (good access from Eastlink) and has good undercover areas.
Thanks for this (and all your suggestions!). Park it is then.

I remember lots of picnics at Jells Park as a kid. Good times.

I'm in the inner west now, so am looking up similar facilities on my side of town. Hopefully will find something along the Maribyrnong River!

Thanks all!