Following up on the last post, Melbourne in a Day, Rachelle, a Melbourne local, describes additional things to see if you have more than a day in the city…
Carlton Gardens: Within the city there are a number of beautiful areas to see if you have the time: Carlton Gardens houses the Royal Exhibition Building, which hosts many events and has a beautiful exterior and interior, and the Melbourne Museum sits directly behind the exhibition building. This is one of the few museums you have to pay to enter (~$15pp), but is a very fun 1/2 day if you have kids! This are is just north of the central business district (CBD) and is located in Fitzroy. Still easily accessible by tram (~5minutes)!
Brighton Beach: This small beach-side community is famous for its colorful bath houses and relaxed, but up-scale feel. To get to Brighton, take the Sandringham train on PTV and get off the the Middle Brighton stop (approximately 20 minutes on the train from the Melbourne CBD). The town of Brighton is waiting for you just off the platform with lots of restaurants and shops (try Half Moon for lunch if you don't mind a pricy meal, or head to the closest butcher shop where they will surely have a sausage sizzle on the sidewalk for about $2/snag) and the bath house beach is about a 10 minute walk. If you want to skip the bath houses and just head for the beach, take the train one stop further to the Brighton Beach stop, and you will see the ocean as soon as you step off the platforms (the drawback being no beach houses on this stretch of the coast).
Fitzroy Gardens (not actually in Fitzroy): This is an enormous park at the eastern edge of the city and is home to some of the city's best trees. If you want to go for a run, this is the best place in the city to do it!
Places to visit around greater Melbourne
The Great Ocean Road: If you are willing to get on a tour bus and spend a bit more money, some of the most spectacular scenery you will every see lies just west of Melbourne along the Great Ocean Road. Home of the 12 Apostles rock formations (only about seven now remain), this scenery matches that of the Amalfi coast. Loch Ard Gorge and Gibsons Steps are two sites you will not want to miss along this trek. The site of the 12 Apostles lets you look out over the formations, while Gibsons Steps lets you walk along the coast and look up at the massive structures. WARNING: If you are prone to motion sickness, you will need to bring a large bucket or take a hefty dose of Dramamine prior to setting out on the Great Ocean Road!
Phillip Island: Every night on Phillip Island "rafts" of Fairy Penguins come in from the water and you can sit on bleachers along the waters edge to watch the action. This is a fun activity, particularly for kids, and if you take the Little Penguin Bus Tour, it's about $75pp, you will get the scenic route to Phillip Island instead of the highway, and a quick tour of the island.