For currently unserved 1-connection markets, MIA is really what we need. JL has been hinting at it too to facilitate Latin America connectivity. DFW and JFK both have 'some' flights to Latin America and the Caribbean but AA operates most of the spectrum from MIA only sadly.
ORD and JFK are already well served by JL, so don't see that plus AA already abandoned HND-JFK once. PHX would really only help with domestic connections but LAX also covers that pretty well currently, short of more domestic discontinuations from there. UA has a lot better Asia to Latin America connectivity by far than AA just because they have flights to both IAH and EWR and serve a huge portion of the region from both airports. That's really AA's weakness, despite having a better network to the region, it's all from MIA which isn't connected very well to Asia. It's a bit of a PITA to get down there now on OneWorld with the loss of LA.