I have stayed at AM a couple of times now, and I would highly recommend it. As the rooms are located in a residential building, it really feels like a home away from home. I most recently stayed in Apt. 401 in mid February 2013.
Self contained, and very well appointed, the kitchen has a gas cooktop with rangehood, oven, microwave, dishwasher, and a full-size fridge. It is kitted out with all the cookware, utensils and crockery you will need if you want to be 'self sufficient' and cook all your own meals (there are IGA and Woolworths supermarkets within walking distance). There is also a small stereo unit with iPod dock on the kitchen benchtop which is a great touch. Oh and there is a dining table with seating for four!
However, given its fantastic location you are within minutes of Chinatown, the Greek precinct, and the centre of the city for all manner of culinary delights. Its so easy to jump on a tram and be connected with Lygon Street in Carlton, Federation Square, the Arts Centre, Southbank, or cross to the other side of the city to Docklands.
Inside the apartment there is a fantastic couch setup to stretch out upon, a big screen LCD TV & DVD (with a selection of discs on offer) but there is no pay TV just the digital free to air, but this is not an issue in my opinion. The bedroom is really nice and comfortable and there is plenty of robe space and coat hangers provided. The bathroom is quite spacious (featuring a large shower recess - no bath) and also includes a washer & dryer which is extremely handy for longer stays and another aspect which truly enables you to be self-sufficient within the apartment.
There are not many negatives, but as has been mentioned by others, the free-standing AC unit in the living area is very noisy, and while the west facing apartments can get quite warm in the afternoon in summer, it doesn't take too long to cool the room down so you don't have to put up with the AC noise for long. The windows are treated with block out blinds so they help reduce the heat load. There is a fan provided for the bedroom.
Personally I don't have a problem with it, but you need to be aware that being in the heart of the CBD, and above a laneway with bars and restaurants, there can be some noise from late night revellers, and the sound of rubbish trucks and glass bottles being collected in the early morning. Having said that, there was very little noise coming from adjacent apartments. As it is a modern, Architect-designed building, you can expect that the construction conforms to current standards and has good acoustic separation, given that it is a residential tower.
Overall, with what is provided in the apartments, I have found that they are excellent value for money. If you don't mind not having a reception desk and sometimes having to check yourself in (keys left for you in a lockbox in the lobby) if arriving out of business hours, but instead rather than feeling like you are staying in a motel/hotel you have your very own 1-bed apartment in the heart of Melbourne, then About Melbourne Apartments is the place for you!
Now I am tempted to try one of the larger penthouse apartments ... :)