Melbourne aquarium is a great aquarium (I much preferred it to Sydney's - I didn't constantly feel like they were trying to squeeze all the money they could out of me).
The antarctic section is great (penguins!), and the place is really well laid out.
The aquarium is in town, and the easiest way to get there would be to train to Flinders Street Station, and then tram south to King Street. Alternately you could train to Southern Cross Station, then walk two blocks south along Spencer St and then one block east along Flinders St
Entry fee was $32 from memory - it was definitely worth it. about 9 years ago
I agree with Jaidev S we really enjoyed the aquarium when we went. It is quite large and has many different aquariums reflecting various habitats.
Depending on where you stay it is quite easy to walk to the Aquarium, we did it with our two children (14 and 11) and had no problems getting around Melbourne.
Tickets are a bit expensive ($32.50 for adults) but some of the tourist brochures you can pick up from the t\Tourist Centre at Federation Square have discount vouchers.
It's a good idea to visit the Tourist Centre as they have a lot of good info available. about 9 years ago