The most famous and probably the most visited beach in the vicinity of Melbourne lies in the suburb St. Kilda on Port Philip bay. Due to its popularity it is sometimes called "the Bondi of Melbourne" referring to the famous beach resort near Sydney. It was developed mid 19th century to give the wealthy Melbournians the opportunity to flee the ever growing city and enjoy the cool sea breeze in their stately Victorian cottages. You can still see quite a few of them when you wander around.
Later, at the end of the 19th century, the decline of the town happened when Australia had its great depression due to the fact that the major source of income, the gold arteries, came into depletion. The beautiful houses went into decline, the few rich people not touched by the depression left the town, and the streets of St. Kilda became notorious due to the growing presence of brothels and gambling dens.
The beach is decent and the sea water is fine, but it's definitely not the best beach in the country, so I wouldn't linger here too long. There are a few interesting sights in the town like the old Luna Park, with an entrance through an open mouth, the Esplanade Hotel and the Pier. They are all located on or close by The Esplanade next to the beach.
If you can, you should come here like we did the 2nd Sunday of February when the annual St. Kilda Festival is held. There was a market, a motor show, street stalls and live music. The atmosphere was like a real carnival. The weather was great that day so there was an incredible crowd filling the street of this beach resort.
It is a good side trip from the city, at a distance of a few miles. To reach St. Kilda from Melbourne it's best to take a tram from Bourke Street directly to the Esplanade. There are also a few city buses going this way. The drive there is mostly along Port Phillip bay and offers some nice views on the Melbourne skyline, like the one from the St. Kilda Yacht Club.