Are there any army bases from mexico to south america?

Yeah not much of anything. Might want to look into maybe San Jaun, P.R. where the 192nd Infantry Brigade was based after it was withdrawn from Panama, with the Naval training near by. One thing you would have to watch out, there was/is faction that want independence for the Island from the U.S., and sparks up every so often.

There are few small joint bases that are mostly not advertise as mentioned, and need the MOS specialty to get the slot.

Best bet would be try to get to Spain if you can find slot to get over there.

Soto Cano Air Base, Honduras

It's actually a Honduran military base with a small US Joint military presence. I was stationed there for a year, one of the most rewarding years in my military career. It is a 1-year (with the option to extend) dependent restricted tour (like Korea was), however we did have a couple people (also Latino) that paid for their families to come down on their own dime. Cost of living is cheap, but of course because it's not command sponsored, everything would be out of your own pocket. If your family speaks Spanish though I'm sure you would be able to make it work without the logistical support that normally comes from the military overseas.

Send me a message if this is something you'd like to know more about. The base living conditions are austere, but the mission is incredible and it's like nothing else you'll find in "big army".

As far as I know the US Armed Forces has no permanent bases in Mexico or Brazil.