The beautiful and historic Fitzroy Gardens (the website needs a good update) are located in East Melbourne near the MCG, and provide a fantastic backdrop for a lazy afternoon of picnicing along with a number of interesting attractions.
With plenty of open space to spread out a picnic blanket the park also provides a playground for the kids, toilets, and even a cafe.
There is also a miniature Tudor village, the carved Fairies Tree, and of course the gardens themselves.
To get to the gardens from Federation Square
Take tram 48 or 75 from Flinders Street or the train to Jolimont Station and cross Wellington Parade. Otherwise you can usually find some street parking nearby.
Why? A lovely spot for a picnic, with a number of diverting attractions, makes for a relaxing lazy afternoon.