Explore more of Lima, the city is overlooked but offers tons to do.
To see all the sites in Lima would require a stay of about a week - that is how much there is to see and do. By far, Lima's gastronomy is its best attraction.
As far as safety goes just try to blend in with the locals and do not be paranoid, not everyone is out to steal your camera, etc.
Finding a good guide is key to making any visit to Peruan incredible one.