Go to Eureka skydeck on southbank. Amazing views of the city. St Kilda is great, shops and bars and restaurants etc.
Melb Zoo is well worth a visit, great zoo. Healsville Sanctuary is also great. Great Ocean Road day tour? Spectacular coastline! The Dandenongs National Park is beautiful to go for bushwalks. Phillip Island is good too, go and watch the Fairy Penguins.