Per this Flyertalk thread, there are currently some great fares from both New York and Miami to Iguassu Falls, Brazil (IGU) this winter starting at only $474 round-trip on both LAN and TAM.
Finding Airfares Using the ITA Matrix
One of the most useful tools for searching airfares quickly is the ITA Matrix
For a quick sampling, I searched airfares from New York (JFK) to Iguassu Falls, Brazil (IGU) and was able to find these fares for 4-7 night stays starting at $474 in January.
Once you find your desired flights, you can then head over to Expedia, where you can book your flights, since you’re not able to book flights through the ita Matrix.
If you signed up for the Barclays Arrival World Mastercard the sign up Bonus of more than $400 travel credit after completing the minimum spending can get you to Brazil for almost free. You may also consider signing up for the Capital One Venture Rewards card which also comes with a $400 travel credit after completing the minimum spending requirement.
I always like to keep the Arrival and Venture card handy for these miscellaneous expenses which otherwise cannot be redeemed using miles (taxes, fees, baggage etc)
You don’t have to but I am grateful if you plan to use my referral link to sign up for these cards.