Flights at this price are available on select dates starting in late October through the end of April, with the best availability in January and February.
Searching AA.com, we found seats departing AUS on Friday, February 1 and returning from UIO on Monday, February 11, 2019. Flights connect via Miami MIA on American and Houston IAH on United. You can make it a 2-for-1 trip on American if you'd like to have an overnight in Miami, if not avoid those fares that require long layovers.
See our fare listings from Austin (AUS) for a complete look at current finds to both domestic and international destinations.
Need a room in Quito? Here's what's available for the above dates on Hotelwatchdog.