A day trip to Philip Island for fairy penguins and seals, gorgeous scenery and food.
You can also see fairy penguins at the end of St Kilda pier at dusk. It's a nice suburb to spend an afternoon... beach, amusement park, amazing Jewish cake shops on Acland St. Great boardwalk with restaurants for a sunset drink.
In the city, wander around Southbank and the arts precinct, there's a market on Sundays, and along the river to Birrarung Marr on a nice day. The art gallery is free.
The museum is fantastic kids and useful on a rainy day, as is Scienceworks. Melbourne Zoo also very well done.
Definitely 2-3 days to do Great Ocean Rd, making sure you spend time at a lovely surf beach like Lorne, around to the Twelve Apostles, and inland to the rainforest in the Otway Ranges (check out Otway Fly and treetop walk online).
Try to get the kids minded and go to a spring horse race event, Melbourne Cup is crazy busy but Oaks or Derby day around the same time is also fun.
Other cool day trips could include Peninsula Hot Springs, a bushwalk (You Yangs, Macedon Ranges or Dandenongs depending on which side of Melbourne you're on), ferry to Williamstown for lunch and for grown ups the Yarra Valley wine trail.