Lima is a dusty, dirty, treeless dump, and pretty dangerous to boot, and I'd land at the airport and transfer direct to Cuzco which is one of the great cities to visit on this plant.

The Hotel Las Ruinas right atop Macchu Picchu is the ONLY one up there. INSIST on it! All the millions of day tripper plebs swarm together down in Aguas Calientas in the valley.

You'll be wandering the Inca Trail at dawn and have the place to yourself and Llamas and the spirits until the dozens of buses bring 1000s of tourists up at mid morning!
http://www.ozemail.com.au/~ozstamps//llamas.htm