I would start the day with one of Melbourne's best offerings - coffee!
We make the best in the world (slightly biased, but I've never had better in any of my travels)
Jump in a cab and get dropped of at St Ali in Sth Melbourne or Seven Seeds in Carlton. There are other contenders for the 'best' but I happen to like the food at these places too. The other place I like, where the coffee isn't the best you can get (but pretty good) but makes awesome breakfasts in Brasserie Bread in South Melbourne.
After breakfast, head into the centre of the city, take a stroll along the banks of the Yarra River to help digest breakfast and then jump on the free tourist shuttle bus. It's a free HOHO service.
thatsmelbourne.com.au/gettingaroundthecity/v…
Hop off at any or all of the stops and tour around the sights.
You probably won't feel too much like lunch, but if you ant something to eat, any of the restaurants along Southbank will offer you nice river views and a chance to rest your les.
One of my favorites for location is the Riverland Bar, on the north side of the river http://www.riverlandbar.com/
You can have a light lunch or just a cooling drink.
After lunch, you can either continue with your HOHO experience or pop into the tourist office at Federation Square (just above the Riverland Bar as it happens). They sell a booklet whose name escapes me, but it's about $8 and is a self guided walk around the historic buildings of inner Melbourne.
The people who work there will know it.
Alternatively, on the That's Melbourne website (above) there are downloadable self guided tours you can take complete with PDF brochures.
If history doesn't ring your bells, you may want to spend a couple of hours wandering through Melbourne's back lanes and alleyways (not dangerous and very trendy).
If you like walking, then perhaps head through Albert Park and around the lake, down to St Kilda and take a long walk along the beachfront back to Port Melbourne to get back on your ship in time for a well earned dinner.
Have a wonderful cruise.