ANU. No contest. If you want to do anything related to politics/IR (admittedly not my area), then ANU is the place to go. The overwhelming majority of ANU Arts students seem to be aiming for a career in foreign affairs/politics/international development. The prime minister went there, which is where he learned Mandarin. Also, if you're interested in Asian Studies they have an awesome library collection (second only to the National Library, which is about 5-10 min drive away.)
Academically ANU has a better reputation - well, it has a reputation as the hardest university in Australia. Uni Melb is known for having extremely high entry standards, but ANU seems to be harder once you're in. If you're interested in academia/research, then it's definitely a good place.
re: location. Yes, Melbourne is an awesome city. By far the best city in Australia. But Canberra is the capital city, packed with politicians and diplomats. It's also a good place to be a student - students make up a relatively large portion of the city and ANU has a good campus atmosphere and sense of community (better than Uni Melb, but it's also much smaller). Canberra is a bit country-townish, except that it's populated with over educated left-wing people. If you need a big city fix, it will take about 3 hours and $15 on the bus to get to Sydney. A plane to Melbourne will cost you $50-100 and take less than an hour.
Edit: If it's the MIR you got into at Melb, I'd recommend steering clear of that dept. I know a couple of people who did honours there (which is being phased out, I think, in favour of the MIR) and both had issues with supervisors getting switched mid-way through their thesis. It doesn't seem like a particularly student-friendly or supportive department. Also, the Masters is just a glorified/longer version of undergraduate honours, because they are ditching honours degrees and making people stop undergrad at a 3-year degree and then do a Masters.