American Airlines has low fares to several airports from Los Angeles to Panama PTY ($383), Bogota Colombia BOG ($514), Quito Ecuador UIO ($603) and Rio de Janeiro GIG ($629). Rio is even lower from SFO at $615.
These fares are for departures in late May to Quito. and early June. Bogota, Panama and Brazil fares to Rio and Sao Paulo go into summer. These are all economy Q booking class and earn 100% redeemable miles with American AAdvantage.
Los Angeles LAX – BOG Bogota, Colombia
$513.60 May 30 – June 10, 2015
7,347 flight miles (7 cents/mile)
Los Angeles LAX – Quito, Ecuador
$602.81 May 30 – June 10, 2015
8,256 flight miles (7.3 cents/mile)
Los Angeles LAX – Panama City, Panama
$379 May 27 – June 4, 2015
6,987 flight miles LAX-MIA-PTY-MIA-LAX (5.4 cents/mile)
There is competition with Copa and United on this route where those airlines might have lower fares.
Los Angeles LAX – GIG Rio de Janeiro, Brazil
$642 June 10-17, 2015 (purchase on US Airways site for lower fare)
13,766 flight miles LAX-MIA-GIG-JFK-LAX (4.7 cents/mile)