I have stayed at the FP Miraflores and the Sheraton. While Miraflores is a much more pleasant place to stay, many of the historical sights of Lima are downtown, where the Sheraton is located. We got a walking tour of downtown for one morning, and in the evening went to see the nearby water fountains which is a nice local family experience. The main thing the area around the Sheraton is lacking are good restaurants, but if you take taxis for dinner you won't suffer with traffic as much. The Sheraton had a great breakfast (comped for Plats), but rooms were dated, although it's a great deal on points, and nearer the airport, as stated.