See interesting films at the Art Deco-styled Astor Theatre in St Kilda. There are several moonlight cinema programmes in summer. The Melbourne International Film Festival is on in August.
Alternately, visit the Cinema Nova on Lygon Street (tram 1 or 8) on a Monday for $6 films before 4pm.
Visit a comedy club. The Comic's Lounge has shows for $10-25 including a show filmed for Channel 31 on Mondays, or dinner and show for $45. The Comedy Club has dinner and show for $32 and shows only beginning at $7 (discount ticket price).
Watch the mesmorising process of personalised hard candy being hand-made at Suga. Around lunch time is a good time to see (and sample!). There is a store at Queen Victoria Market, but if you visit the Royal Arcade location, you can also watch chocolate making next door at Koko Black.
Watch a game of AFL football at the MCG or Etihad Stadium during the winter, or a Cricket Match during the summer.
Kick back at one of Melbourne's fantastic cafes in the CBD (Degraves St, The Causeway, and other laneways are fantastic for this), South Yarra (Chapel Street) or Fitzroy (Brunswick Street, Smith Street).
Melbourne has an exceptionally vibrant live music scene. Many bars and pubs will have copies of the free magazines "Beat" and "Inpress" which provide local gig guides. Fitzroy, Collingwood and St. Kilda are generally your best bets for seeing some of the great local talent Melbourne has to offer. Venues where you generally can't go wrong include: "The East Brunswick Club", "The Evelyn" and "The Espy".
You could try hitting a round of 18 hole Mini Golf, that has been designed around an Australiana theme and is indoors and under Black Light with state of the Art light and sound system with fluorescent colours, The Black Light Mini Golf is located at the Docklands, Just behind the Big Wheel (although note that the wheel is currently dismantled due to a fault, and won't be rebuilt until early 2011). Being located indoors means that you can play all year round, Admission pricing is $13.00 an Adult and only $10.00 a Child and takes around one hour to play.