Well, while you're in Melbourne, you can...um...
there's the Puffing Billy railway if you like narrow gauge steam engines...and...um...
there's a science museum which is also nowhere near the city centre...and...
you can get some nice Italian food on Lygon Street.
Oh, I suppose you could visit the Melbourne Cricket Ground, which is a pretty impressive stadium in its own right, although there won't be any events on there while you're in town...
:-)
= = = =
In case you weren't aware, there's a long-standing rivalry between Sydney and Melbourne. And although I don't live in either city I've been to Sydney many times more than I've been to Melbourne, so I know its tourist spots better.