I am not from Melbourne, however I can recommend:
- street art / graffiti in the laneways, also if you have a good walk around you'll find cafes and restaurants in other lanes and alleys
- Koko Black hot chocolate in Royal Arcade
- Queen Victoria markets, it also has a Koko Black however that one only sells chocolates
- NGV @ Fed Square is good, although I have not been to the main NGV building on the other side of the river
- in Fitzroy there is a pool/billiards hall that is not licensed, so no alcohol around instead a quiet pool hall that serves coffee
- briefly went to St Kilda beach and South Melbourne beach, they have a nice view however nothing too special
- Ferguson Plarre bakehouse Coburg
I imagine there's more however that's off the top of my head, someone else can recommend something better
Sure, blame the birds for incompetent fishing skills. 
By the way, can you recommend other Melbourne tourist attractions? I am heading there during the Easter long weekend with the family to visit my folks who live near Dandenong.