Although most people interested in biodiversity, plants and wildlife viewing will want to go to the jungle areas (which I don’t know well and am not writing about here) there is also a tremendous amount to see on the coast and in the Andean mountains of Peru and beyond. A one-stop book for the interested tourist is the Peru (The Traveller's Wildlife Guides).
Llamas, Alpacas (domesticated), guanacos and vicuñas (wild)
Llamas and sometimes alpacas, the domesticated members of the camel family that are native to Peru, can be seen and photographed all around the Cuzco area. There are often several around the parking lots at Sacsayhuayman — all dolled up so you can photograph them (for a dollar or five). You have to get a little farther off the beaten path to see them on farms or out in the pastures but you’ll likely see some on any trip through the sacred valley on your way to Machu Picchu. It’s rare to see a real llama train these days, as there are roads providing access to more and more of the small villages around the mountain regions, but small ones are still used to take goods to and from remote towns. You’ll most likely only see them if you go on long day hikes or backpacking into such towns. Check out Lonely Planet Trekking in the Central Andes for ideas. Vicuña or guanaco are most likely seen on trips through wildlife sanctuaries, national parks or on long trips such as the ride to the Colca Canyon from Arequipa.
Other mammals (vizcacha, deer, Andean foxes, etc.)
If you’re really interested in the mammals of the Central Andes, get ahold of Mammals of the Neotropics (Volume 3 ): The Central Neotropics: Ecuador, Peru, Bolivia, Brazil
If you’re serious about birding, the references are Birds of South America: Non-Passerines: Rheas to Woodpeckers and Birds of Chile.
There is also a A Field Guide to the Birds of Peru.
Fossils and more
A starting point that almost no one will tell you about is the Natural History Museum at the San Marcos National University in Lima. The link above is to their website. Although it’s in Spanish you can click on the photos to see details of the collection and preparation of some of the items (large toothed whale, South American horse fossil, etc.) on display there. Although the museum is a little bit sad looking, you can see fossil and living Peruvian animals and plants on display there that you won’t see anywhere else. If you’re interested in the evolution of South American fauna check out Splendid Isolation: The Curious History of South American Mammals.
A list of places to visit for those interested in ecotourism/natural history can be found on the Peru national travel chamber of commerce website. Also see Duke University’s Park Watch site for Peru to get information on the parks and preserves as well as the threats to them.
Also, try the zoo in Lima (the only zoo I know of where you can visit both archaeological ruins and exotic animals in one place. It’s called Parque de las Leyendas (Park of the Legends) — the website is only in Spanish but it has pictures of animals, plants and archaeological features so it can be worth exploring even if you don’t read much Spanish.
Llamas — do you have a llama fetish? Then check out mountlehman llamas site.