The Pisco Sour is the closest thing Peru has to a traditional drink. The base of this cocktail is Pisco Puro (pure), a spirit made of grapes. It is similar in taste to Grappa (Italy) or Palinka (Hungary) and a host of other varieties. I cannot recommend Pisco Puro, but the Pisco Sour it is a nice cocktail.
An excellent place to enjoy a Pisco Sour is El Bolivariano in Pueblo Libre. The High Resolution Rutas Recomendables Combi Map includes a discount voucher for El Bolivariano with which you are entitled to 2 Pisco Sours for free. So make sure to bring someone along!
Pueblo Libre has a totally different feel from Miraflores. It is worthwhile to make a trip to Pueblo Libre, if only for the Pisco Sours in El Bolivariano. But apart from that you could also visit the excellent Museo de Arqueología, Antropología e Historia del Perú. The museum is pretty much next door to El Bolivariano.
Please note: a Pisco Sour is an alcoholic drink. Drink Responsibly.