Lima, a massive city of 8 million people and counting, is a place that deserves one day and one night of exploration. It is city with a troubled recent history, but one that is changing every day. With one day, I'd suggest doing a guided tour of the historic center, with its presidential palace, cathedral where conquistador Francisco Pizzarro is buried, and its glorious South American city square, Plaza de Armas. I'd also tour the Monastery of San Francisco with your guide, a short drive from Plaza de Armas. You cannot miss the stunning historic home, Casa Aliaga, near the main square. The home has been in the same family since 1535, when Pizzaro founded Lima. One of his captains, Jeronimo de Aliaga Ramirez, was able to build his home next to Pizarro's house, and 17 generations of his family have lived in it since. The rooms are filled with original treasures and artwork, and I loved seeing Captain Aliaga's personal sword on display. When I was there, family members were also roaming the home, though their personal living quarters are not open for touring.
I suggest staying in Miraflores, and this is where you'll have great ocean views, and access to shopping (the mall is called Larcomar). If you eat at one restaurant in Lima, make it Astrid y Gaston. I took myself out to lunch here and had a great time. Chef Gaston Acurio is known for his haute Peruvian cuisine, is sometimes called the "Jamie Oliver" of South America, and has opened restaurants in Ecuador, Argentina, Colombia, Chile and more.
I missed Lima's many museums because of time, but have heard incredible things about the Museo Larco Herrera, with thousands of ancient Peruvian treasures on display.
With each hour in Lima, I felt an incredible buzz of a city on the verge. I know that if and when I return in 5 or 10 years, the city will be completely different. They are completely cleaning up and redeveloping park area near the ocean, and more and more businesses are coming in. I met at least 10 American and British business travelers, all coming to start or support businesses in Lima. There is huge growth opportunity. Peruvian cuisine is one of the hottest trends in restaurants worldwide right now, and much of that is coming out of Lima.