Ah, I forgot about tennis. I applied to UMelb and Monash back in 2011 when I was applying to grad school, but was scared off by some attacks on Indian students at the time. My sports watching life would've been so different if that had gone well.
I'd put London slightly above Melbourne, it's got Tennis, Football and Cricket among others.
One thing to note is the accessibility and convenience of the events in Melbourne. The MCG and other stadiums/arenas are all in a big complex right in the heart of the city, with easy train, tram, bike, and walking access, and this includes the Australian Open tennis. The Grand Prix is in Albert Park, which is kind of like saying there's Formula 1 in Central Park NYC, kind of nuts.
Not sure about London, but in NYC, the sporting events are far away and a real drag to get to. US Open tennis is in Queens - take a subway for an hour from Grand Central, then walk a mile on a boardwalk to the stadium, and when I attended a couple of years ago the fan experience outside of the actual matches was pretty poor (and this being the US, all about promoting corporate sponsorships). NFL football is actually in New Jersey, you have to take a commuter train from Penn Station out there and back. Madison Square Garden for basketball is the exception, but the ticket prices are prohibitive. Baseball is in the Bronx, which is not so bad, but I haven't done it.
You don't even have go to Albert Park for the Grand Prix, you can hear it from the CBD! ;)
But I concur, I have never seen a city where all the major amenities are all so closely located to the city center, it's fantastic. Etihad Stadium, Melbourne Cricket Ground, AAMI Park, the Australian Open, Hamer Hall, Sydney Myer Music Bowl, State Library of Victoria, Melbourne Museum, National Gallery, Queen Vic Market, Federation Square, Birrarung Marr, Royal Botanic Gardens, concert venues, theatre district, Chinatown, Greek precinct, Little Italy, Little Saigon, University of Melbourne, RMIT, Docklands, South Melbourne Market, the list goes on and on...
I'd put London slightly above Melbourne, it's got Tennis, Football and Cricket among others.