The inner northern suburbs represent great value, just outside of the city. You can pick up a standard 2 bedroom apartment for around $500k-$600k in Carlton, Carlton North, Fitzroy or even Melbourne CBD. The inner north is leafy, with parks aplenty, a plethora of transport options and the mecca of cafes, restaurants, bars and pubs.
Don't be afraid to reach out if you have any questions about any other inner city suburbs. Melbourne is full of choice near the CBD!