Lares Trek

This remote and rarely visited region offers the trekker an insight into the real lives of the Andean farmer, dressed in their traditional brightly colored ponchos. You’ll have the opportunity to see thatched stone houses surrounded by herds of llamas and alpacas. Inside the houses you’ll see guinea pigs running loose.
http://www.lares-peru.com/
The advantage of this trek is that permits are not required and, in theory, you could just turn up in Cusco and make a booking 2 or 3 days in advance. http://www.lares-peru.com/ However most companies are combining these treks with a visit to Machu Picchu and therefore train tickets between Ollantaytambo and Aguas Calientes are best bought several weeks in advance.