I arrived at Lima's airport and had one full day to discover this capital. I really enjoyed walking in Miraflores. It has a beautiful Kennedy park, is surrounded by high-rise buildings, and has a boulevard overlooking the ocean. Lots of people doing sports, walking around, or enjoying street food (I tried a nice crepe). There are a lot of theaters, restaurants, and bars, which make Miraflores the place to go for a good night out. There is also lots of green areas for a midday nap.
In Miraflores, there is a sweet spot called Parque del Amor (Park of Love).
Another place that I enjoyed a lot was Larco Museum which shows an amazing collection of pre-Columbian art. The best part of it was (unexpected) pre-Columbian erotic pottery (try to have a guide or audio guide to understand everything the what's and why's).
Also, even if I didn't have lots of time, I visited Plaza de Armas (Plaza Mayor), which is a historical center of Lima, and its Cathedral next to it.