South America is such a diverse continent that it's difficult to imagine that you would let the cheapest airfare dictate your destination, especially for a trip of six to eight weeks in length where the airfare won't end up being the biggest component of the overall cost.

Generally you'd expect that the cheaper airfares from either NYC or the Bay Area would be to the northern part of South America, probably Colombia, Ecuador or Peru (I'd avoid Venezuela and the Guyanas for reasons of security). For these destinations you could check for cheap fares on AA, Copa (hub in Panama City and codeshares with CO), LAN and perhaps Avianca (for Colombia specifically). Try out the following website:

http://www.vayama.com/

Plug in a few destinations and see what comes up.

If security is a big issue for you, Chile is the only place in SA that I know where you can move about with almost as few security concerns as in North America. That said, single women can and do travel widely throughout the continent and if you take the normal precautions you'll likely be ok. It certainly helps if you speak the language(s).

As for me I'm a big fan of Peru. It's a very diverse country with a fascinating history and a lot to see and do, not to mention great food, and it can be done on a budget. You could easily spend two months there exploring the coast, highlands and rain forest, as well as sites of historical and cultural interest like Machu Picchu.