I'm planning to travel alone in August or September to either Chile or Peru. Any recommendations on which country is better for traveler who likes to venture from the tourist path (safety? language barrier? etc.) and which month is the better time to go. What are the "don't miss" sights for each place? Nightlife? Inexpensive places to stay? Activities? Any information is appreciated.

August/September is the best period to visit the Peruvian Andeso not miss Cuzco,Puno and the lake Titicaca,Arequipa and of course the wonderful Macchu Picchu. On the coast there is the GARUA, the typical peruvian thicky fog: as a result I do not think that you would appreciate it.
Trujillo in the north is worth a visit: it is a really nice colonial town.
Before going to Perù you should study a little spanish ( "survival level" is enough) as only a few peruvians can speak a few english words.
Go to Cuzco by plane from Lima or Arequipa, paying attention to the fact that Cuzco is very high (mt.3200). Going by train from Cuzco to Puno is very interesting (the landscape is marvellous)but exhausting as it takes more than 11 hours and the trains are not comfortable at all even in 1st class.

I agree with Nicola. You must not miss Cuzco and Macchu Picchu. Another side trip I would suggest is flying from Lima to Iquitos in the selva (northern Peru). From there, you can take boat trips down the Amazon. Buen viaje.