>>>> Central Lima is pretty cool, and like Corsaire said, keep a very low profile. You may want to visit the Museum of Italian Art, the catacombs, Cerro San Cristobal, Parque de La Muralla and the rather disturbing, to say the least, Inquisition museum. <<<<<
BTW, when I visited Plaza de Armas (Lima Center), where the Goverment Palace is I saw they have mini tours to Cerro San Cristobal from there, on a good clear day you can have a very extended visibility of whole Lima, plus they have up there a Cafe / Deli, and it's only S/. 5 or 7 soles round trip, can't beat that.