Plenty to see in the city and depending on how far out you want to travel.

If you're public transporting it, get your head around the myki ticketing system - being an out of towner isn't an excuse the ticket inspectors take and you don't want a $75 on the spot fine.

Crown Casino area and Southbank good for restaurants and cinema, and the Chinatown area is pretty good too for eating. The food truck scene is growing but you need to chase them down.

Do not bother with the Melbourne Star observation wheel. Just don't. Eureka skydeck is a better option if you want a view.

If you're a sports fan, the MCG tour is worth doing. Maybe check out the Queen Vic market.

See also the suggested shops list

And a fan meet on the weekend could work. What dates are you in town?