I'm not familiar with South America, but 80-90% of Europe would be safe enough as long as you purposely don't choose the worst neighbourhoods to live in. South Europe is significantly cheaper than the north though and for American learning Spanish is probably more useful than any other language. I would probably choose a coastal location (Granada is inland), Alicante perhaps or Valencia.
South AmericaI am familiar with (EDIT: part of) South America, and frankly it's sketchy. I studied abroad in Quito, Ecuador; it's beautiful and wonderful to be in the tropics. I've got a friend hanging out in Chile right now
http://southlatitude.wordpress.com/, and I miss the Southern Hemisphere when I read her posts. I miss having a touch of indigenous culture and the beauty of the cloud forest, rain forest, and the Galapagos.
When we jumped into the ocean to hang out with the dolphins who were following the wake of our boat:
When we were in the cloud forest:
I'll probably go back at some point, but I would not take young children there. One of the kids who was also studying at the Ecuadorian university got mugged 7 times while we were there.
SpainI also studied abroad in Valencia, and I loved it. It was wonderful to be a 10-15 bus ride from the warm sea. I did my homework on the beach.
Buck and Mrs. Buck chose Granada for really good reasons (see
http://bucking-the-trend.com/moving-to-pomegranate/ ), and it's a pretty good place for their kids.
At a minimum it would have to be cheap (does that even need to be said on this forum?) and safe. Bonuses would be that it is warm as I'm tired of Minnesota winters, fairly accessible from the US so family/friends could visit, and has a non-English language that we are all forced to learn.
Spain is cheap relative to other parts of Europe, and it definitely won't be hit by the same polar vortices that we've been seeing this winter. You aren't too far away from Africa.
Homeschooling while abroad and RE is a very very interesting topic to me. I'm interested in homeschooling, traveling, and FIRE. I have simply never put them all in one place before. Thanks for the inspiration, stuckinMN!