The Sheraton is in downtown Lima, very close to many of the old churches and buildings (1500's ), the main square, government palace, etc. It is a good place to stay if you are interested in sightseing the "old" Lima as it is within walking distance. The Marriott is much newer and is in Miraflores - not as crowded as downtown, closer to the beaches, nice view of the Pacific Ocean, good restaurants nearby.