I also stayed at that Sheraton for my stay in Lima (about a day and a half, a year ago). I didn't get killed, nor did I sit in the hotel all day. The historical center of town is about a 20-minute walk from the hotel, very easy to get to, and worth seeing. There are some great churches and monasteries around, many with super art collections and one, I recall, with a delightfully creepy catacomb complex underneath. We walked around there for most of the day, then took the free shuttle from the Sheraton to Miraflores (it goes right to the beach) to eat dinner out there. Taxis are quite cheap, so you can get a taxi back to the hotel--a restaurant will call one for you if you want.

Lima has some of the best food in South America, actually. The cuisine is very interesting, including Chinese influences from the older immigrant population, foods from the local indigenous population, and of course European-style cuisine. If you do a little research before you go, you can have some great meals. The breakfast buffet at the Sheraton's not bad, either.