Wait a second. Where in Peru, Chile, and Argentina???
Have you looked into which hotel programs even exist in the places you want to go?

You may be suprised as to how little choices you have, unless you're only going to the huge capital city in each country.

For example, in Argentina, if you go to Salta (in the northwest), there's only one chain hotel, Sheraton (part of SPG). If you go to Iguazu Falls (Argentinian side), there's again only a Sheraton as far a chains, but in this case even on points its very expensive (the signup + spend bonus for the SPG Amex card will not even get you two nights there!). Go to the tourist towns in Patagonia that have a chain hotel at all, and it's likely to only be a Howard Johnson (part of WyndhamRewards), but WyndhamRewards is a program where you don't get very much from a sign-up bonus (not even enough for one night in South America!). The only good way to get WyndhamRewards points is to start using them for cheap US suburban motel stays during promos, but even that will take a year or two to build up enough for a few nights in Patagonia, since each promo is tightly capped.

On the other hand, also look into the exchange rates, and how much it costs to get hotels for actual money (in which case you do not need to limit yourself to chain hotels). It may turn out that in some of these places it's not even worth it to consider using points necessarily.