Getting a room is easy enough on weekends, when business travelers are back home. You need to book well in advance, however, during the city's hallmark events (say, the weekend before the Melbourne Cup, and during the Grand Prix and the Australian Open). Hostels in the St. Kilda area tend to fill up quickly in December and January.
You'll feel right in the heart of the action if you stay in the city center, which seems to buzz all day (and night). The city center has been rejuvenated in recent years, and you'll be certain to find plenty to do. Otherwise, the inner city suburbs are all exciting satellites, with good street life, restaurants, and pubs -- and just a quick tram ride from the city center. Transportation from the airport to the suburbs is a little more expensive and complicated than to the city center, however.
If you arrive without booked accommodations, contact either of the travelers' information desks (tel. 03/9297 1805) in the international airport terminal, open daily from 6am to the last flight. Or try the Best of Victoria booking service, Federation Square (tel. 1300 780 045 in Australia, or 03/9928 0000), open daily 9am to 6pm.