I'm a lifetime cyclist, hiker, and walker, and for about 10 years now have lived in Colombia, I have visited, and backpacked, seven other South American countries. I have visited and spent time in more than 200 towns and a few cities in SA. Of the countries I have visited-Colombia, Ecuador, Peru, Chile, Argentina, Paraguay, and Uruguay, with a few very brief incursions into Brazil, you will find Colombia is the only one that can be called 'cyclist friendly'. But even at that, it is nothing like what you are accustomed to in North America. The other countries are in no way cyclist-friendly. Throughout SA the majority of roads have little or no paved shoulder, and if there is a shoulder it will be a not-pleasant place for your bike's tires. Drivers of any type of motor vehicle in SA simply don't know how to share the road with cyclists.
The route I preferred, as a backpacker, was the eastern side of the Andes while in Colombia, Ecuador, and Peru. Northern Chile is simply boring and not pleasant (all Atacama Desert). The drawback to the eastern side of the Andes, called La Selva, is there are just about no flat, level, stretches of road of any decent length. You will be going up/down constantly. The coasts of those countries will be flatter, but not flat, and will be littered, very littered. I don't like the Pacific Coast of those countries. Then you get into Argentina (I backpacked through Northern Arg) and it will be quite mountainous, and before long will flatten out on the way to Paraguay, which will be more flat with some hills, no big mountains. Then Uruguay, mostly flat, with no mountains at all, some rolling hills, and lots of wind. I did not enter Bolivia due to not meeting the entry requirements and not being able to do so at the border crossing I was at. And, speaking of Bolivia, I have read many blogs/sites about how the border people will help you obtain everything you need to enter the country. Don't believe a word of it. At the Salvador Mazza border crossing, they didn't help me with anything at all, they simply gave me a list of requirements and that was the end of it.
I really enjoyed South Paraguay and visiting the various Jesuit ruins, and will go back to that region again.
I was in Uruguay during May and it was cold, especially at night, single digit temps. The Northern Hemisphere summer = the Southern Hemisphere winter. Keep that in mind for your schedule.
As for hostels, if you rely on a book or google maps or online sites you will find only a small fraction of the hostels that exist. The vast majority of hostels have no internet presence. When you arrive in a town simply ride up/down every road and look for hostel/habitación/residencia signs. Residencias are the cheapest, but usually really crappy places. Habitaciones are often the same as residencias or sometimes a room in a house.
Hope that helps.
My website/blog: wiegand.org