Skybus – Melbourne
That is no train services from Melbourne city to Airport. That is very unlikely for a big city. They have Skybus and other coach services.
I used Skybus. That cost $16 per trip(I bought from Blue Holiday, but that is same price to buy at airport). Every 10 mins, there is a bus to city(Southcross station). At Southcross station, they have a free connection service to City hotels. I lived in Holiday Inn on Flinders. That is only a few blocks away. Walking is the fastest way in my case.