Well, Melbourne is much more relaxed than sydney =P Lots of good food and cafe around, if thats your sort of thing.
Docklands is worth a visit, many good restaurants around there. Definitely go by Parliament, and there's a coffee store on Spring street which I high recommend. Its called Pellegrini's, and its been open since the early 50's. I go there everytime I'm in the city.
pellegrini's:
Please wait...
Have a walk around the city. Unlike sydney, Melbourne city is arranged as a grid, so its much easier to find your way around.
How long are you in Melbourne for? You can consider stuff like winery tours. You can also do day trips to the 12 apostles, ballart (which used to be a gold mine town), and if you're hiring a car than I highly recommend driving along the great ocean road. Absolutely awesome drive, plenty of good scenery and lots of spots for you to relax should you feel the need to.
Whilst down in Melbourne, you could to a short trip down to Geelong, which is less than an hour by train and very cheap to get down to. Its very beautiful down there along the sea, and there are some interesting places to visit as well. If you don't mind a longer train journey down, Warrnambool is also very beautiful, especially this time of the year as there are whales.
I'll add to this when I can think of more stuff.