Kensington gets a big tick
Social housing/housing commission flats are permanent fixtures in Melbourne's inner landscape. Richmond, Prahran/Windsor, South Melbourne, Collingwood even the leafy Albert Park all have them. I accept that one might prefer not to purchase in the immediate area of these, but it wouldn't put me off the areas as a result.
Chrissy I realise you are an o/seas investor so your property choices maybe restricted.
For everyone else, for what its worth, the best parts of Kensington imo is the area bounded by Epsom Rd to the west, Macauley Rd to the south right up to Bellair Street / train line to the east. Beautiful period homes, quintessential inner city suburb streets, and you are 2 train stations from Southern Cross/City Loop. On the immediate east side of the train track is also a goer.
Alternatively if you look at the west side of Epsom Rd (which is now Flemington), Bangalore Street, The Ridgeway, Bayswater RD, Westbourne Streets also offer some great properties, although as you go further away from Epsom Rd you go down the hill, as Epsom Rd is almost the highest point in the immediate area.