There are great places to go mountain biking within a few hours of Lima [1], including Pachacámac [2] and the Reserva Nacional de Paracas.
Good bike shops in Miraflores [3] include Best Mountainbikes (Comandante Espinar 320, tel. 01/263-0964, bestint [at] terra [dot] com [dot] pe) and Rent-a-Bike (Marquez de Torre Tagle 107, tel. 01/446-9682), for rentals.
BiciCentro (Av. San Luis 2906, tel. 01/475-2645), in San Borja, is good for repairs and services.
BikeMavil (Aviación 4021, tel. 01/449-8435, bikemavil [at] terra [dot] com [dot] pe), in Surco, rents bikes and leads excursions.
Links:
[1] http://www.moon.com/destinations/peru/lima
[2] http://www.moon.com/destinations/peru/lima/sights/outside-lima/pachacamac
[3] http://www.moon.com/destinations/peru/lima/sights/san-isidro-and-miraflores