When you plan to go to Lima, seriously consider staying in Miraflores or Barranco.
Lima is the city that connects Peru with the rest of the world and with all the other cities in the country. If you wish to venture beyond the airport, then it would be a good idea to choose the places that have a view of the beach. The geography of Peru is divided into three: coast, mountain and jungle. The Lima region is coastal (but not all districts have a beachfront).