Hi Lolly,
When my OH and I went to Melbourne we stayed at the HarbourView Apartments which is located in the docklands area of the CBD area. There's a reasonably priced (about AUS$24 return each)
Skybus Super Shuttle that takes you to the train station on Spencer Street, which is about 5 mins walk from the hotel.
Here's the website
Index but I would suggest booking through a comparison site (I use Travellors Point
HarbourView Apartment Hotel Melbourne - Discount Reservations) as they can get you special rates.
The apartments are quite spacious and really help if you don't want to feel like you are living out of a suitcase. There's a separate bedroom and a kitchenette/lounge room with a shower and toilet room. The free tram runs along LaTrobe Street and takes you into the CBD proper though it's a nice walk in with a lovely little deli/bakery that is part of a cooking school along the way (we used to buy our breakfast or a tea time snack there!)
Hope this helps!