Ok...
Chile is very long... so... in your short time, maybe you can't visit the south... which is very beautiful. So, I recomend you visit the center of Chile: Santiago and Valparaiso. Then you can go to the north: San Pedro de Atacama.
Santiago - Valparaíso: 2 hours trip.
Valparaíso - San Pedro: 20 hours trip.
After thar, you can go to Arica (border chilean city) and cross to Tacna (border peruvian city), and then, visit Arequipa.
San Pedro - Arica: 10 hours.
Arica - Tacna: 1 hour (nothing to see)
Tacna Arequipa: 6 hours. (nothing to see)
Then, of course, Cuzco, and visit Machupichu.
Arequipa - Cuzco... i don't remember... maybe 12 hours.
Then.... i recomend in Ecuador: guayaquil, Montañita... .but, i don't remember so much.
Chile probably is the most expensive of his countries. But, there are good buses here, so you can feel confortable traveling. Peru... not so much, but is cheaper.
You can take a look of this places in google.
I hope to have been useful.... sorry about my english.
bye
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