Hiya,
When we first arrived we stayed here
Darling Towers Serviced Apartments Melbourne (the Caroline Street one) which did the job, clean and tidy etc. It is in South Yarra and excellent for transport (trams at the end of the road and trains from South Yarra into the City). Was also excellent for price as we only needed one bedroom so you can choose the 'get what you're given rate' which is a bit cheaper too - about $90 per night when I looked just now.
Good luck - not long to go now, hey? :)