Melbourne.
I agree with others that a serviced apartment may be more suitable for a stay of a few months. You are unlikely to find a serviced apartment that will give you points in an American hotel loyalty program.
There is only one Marriott in Melbourne but with another planned and a Ritz Carlton being built.
There are however three Starwood hotels.
Westin, Sheraton, and Four Points.
All are good hotels, and you would earn points. With the link Starwood points can be transferred to Marriott.
Four Points is a new hotel, and currently rooms can be had for as low as AUD120 some nights. You could stay there sometimes to get some points, alternating with a serviced apartment.