"There is no plane service, btw."
There sure is plane service - to Juliaca - a 30min to 1hr drive north of Puno. I know Lan and others do this from Cuzco, nonstop or with stops in either Lima or Arequipa.
You can't get off

but if weather is clear this can be a very scenic flight. Did it from Cuzco returning to Lima a few years ago.