Which district are you staying in?
Some depends on where u r staying in Lima. I spend about half my time there and Have an APartment in SURCO near Chacarilla. Miraflores is the touristy district and there are many places to visit there. Lima is like most big cities. Be careful at night but you are fairly safe if you are in these Districts. Miraflores, Surco, San Isidro, San Borja, La Molina and parts of Barranco. I would take the night tour on the MiraBUs to downtown. It is pretty with all the lights at night and sit on the top level. Many great places to eat and very reasonably priced