A lot of places do not let you make reservations online, but you could
call them internationally and make a reservation (if you speak
Spanish, that is). A good place is the New Bask Hostel which I think
is at Garcia and Reina Victoria or Calama and Reina Victoria,
somewhere on that block in the Mariscal district. Its not very private
(shared rooms and bathrooms) for like $7-8. There is also the Hostel
Loro Verde a block over on Juan Rodriguez which is very nice with
private room and bath for like $10-12 a night. That is where I will be
starting on the 17th. Hope this helps.