There's Birdlands Park in Belgrave/Tecoma, just lovely with a lake and all, a double bbq and several picnic tables.
Belgrave Lake with the same facilities (and a cottage you might be able to use?)

In Olinda, there's the Aboretum with a rotunda and bbq's - just next to the Golf Course.

Then there's the Alfred Tindale Gardens in lower parts of Olinda.

Actually, lots of places in the Dandenongs - PM me if you want some addresses etc.