One of my favorite views of the city is when walking/riding up the capital city trail just before swan street:
http://goo.gl/maps/RH7VK
The ever evolving artwork of Hosier Lane, and one of my favorite restaurants, Movida:
http://goo.gl/maps/5gawX
Always pay attention to the laneways in Melbourne. Walk down each one you never know what you will find, like this little cafe:
http://goo.gl/maps/sJOmQ
http://www.thelittlemule.com/
Melbourne Cathedral - from front it doesnt look that big, but quite impressive from the side view. Up at top end of Spring Street. (make a detour to Spring Street Grocer for some amazing homemade Ice Cream & Cheese Room).
http://goo.gl/maps/AfVgb
Brighton Dog Beach - if you have/get a dog. Best fenced in dog beach in Melbourne area, can be hundreds of dogs here on a nice summers day.
http://goo.gl/maps/uzSF0
So many places along the Yarra River to walk and enjoy the scenery:
http://goo.gl/maps/z75Q6