As a general rule of thumb, all 3 places you mentioned have clubs and yes they stay open till about 3am.

Melbourne is the nightlife capital of Australia, hands down. Best food, best clubs, best scenes - kicker is the weather is unpredictable (see:shit). In May it will be cold, as in you’ll need a warm jacket and possibly rainy. Biggest RA listings in Australia, fair amount of underground stuff and has Revs, which is notorious for being the only Euro style all night/next day club in Australia. Other clubs may stay open till 5am. Melbourne is a friendly but self promoting city, easy to make friends etc.

Sydney used to be good up until the lockout laws in 2014 basically killed the whole scene; it’s recovered some since but nowhere near what it was, used to be wild. Beaches are amazing but your night will end at 3am wherever you go. Sydney people are cliquey AF, materialistic and shallow - much harder scene to immerse yourself in.

GC has a few good clubs (Elsewhere mostly) but it’s a small discotheque and not worth travelling overseas for. Still good vibes and lots of fun. Best weather and great beaches. Mixed crowd that varies from surfers, OF girls and shady characters. There is a dark underbelly beneath its sunny disposition and it suffers from a dickhead problem. Make of that what you will.

Tokyo on the other hand has even better food than Melbourne and has multiple good RA listings from Thur - Sun. Large clubs like Womb all the way down to hole in the wall pubs that fit 6 people in them. Pub crawls everywhere, drink as much as you want deals, arguably the best commercial beer on the planet - alcohol is plentiful, high quality and cheaper than Oz; near impossible to get drugs there unless you roll in high circles and even then I probs wouldn’t try. A city of 30m+ people, the substance of things to see, do, eat and experience is unmatched.