Food: N. America, for the sheer variety.
...but in terms of the authentic, native cuisines: Asia
Weather: Europe, at least for now. They're starting to have scorching Summers too, which are my bane. Still, I could flee to Edinburgh or Stockholm in the Summer and probably be fine. I don't know where I could go in N. America to escape the heat.
Movies & television: N. America
Music: N. America. The UK by itself is huge in a couple genres of music that I adore, but if I'm pitting the continents against each other across all genres of music, I have to go with N. America. I honestly can't name a single European jazz or hip-hop musician, off the top of my head (I know there are some, but they don't jump out at me).
Sports: Europe
Natural environment: Tough one. N. America, Africa and Asia seem to run away from the rest for variety, sheer scale, and wildlife. Australia is competitive, and of course S. America has the Amazon river and rainforest.
Languages: Europe. Obviously English is my native language, and the only one I speak fluently. I can get by as a tourist in French and Spanish. I'm not conversational, but if I was living there and taking classes, I think I'd be okay. I could see myself learning German or Italian - again, if I was living there - at least enough to get by. I tried a semester of Japanese once, and my brain nearly leaked out of my ears. And at this point, I think I could spend the rest of my life studying Mandarin or Hindi and be at the reading level of a 6-year-old.
Cities: Europe. New York City is my favorite city, but Europe has multiple cities I'd like to visit. There are a lot of American cities that seem like fine places to live, but I have no reason to visit.
Overall: If I could just live anywhere I pleased, I'd go to Europe for a while, and I could see myself never returning. "I came here for a visit; that was 40 years ago and I'm still visiting" type of thing.
p.s. Shouldn't Australia be Oceania?