In Lima, don't forget to visit La Mar for lunch and Astrid & Gaston for dinner. These are both owned by Gaston, a sort of peruvian version of Emeril. Both are excellent restaurants. La Mar is located in Santa Cruz, San Isidro on La Mar avenue. A&G is in Miraflores by Parque Kennedy.

If you are staying at the Marriott, obviously check out the nice sea-cliff mall right in front called LarcoMar.

In Mancora, I stayed at Punta del Mar this past December and liked it a lot. It is not in the Mancora town and is about a 5 minute moto-taxi ride away, which is a good thing if you want privacy. I'd pay more and get the ocean front rooms. http://www.puntadelmarperu.com/punta_e.php