We're going to Rio over Labor Day weekend. Rio was my wife's first pick while I would rather have gone to Buenos Aires. As this was our first time to Brazil, we needed to get visas. I mailed our passports off on Monday the 9th (along with a money order for $220). I expected it to take a couple of weeks, but we received that passport back on that following Saturday, the 14th. It only took five days to process. They're good for five years, so I'm sure we'll return again.
No matter where you end up, you will enjoy yourself. Did you look at Santiago or Montevideo? We went to Santiago and had a great time. We spent most of the time outside of Santiago though. Anywhere down there would be enjoyable.