Originally Posted by Pedro M

1) I would recommend you take Taxi Green - it s right after customs, and before you exit the airport. It will cost about 50 Nuevos Soles (a little less than $20) to go to the Sheraton and they have nice/safe cars. Don't take a taxi from outside the airport.
2) Unless you are in the nicer parts of town, few people will speak English. You won't have a problem at the Sheraton. I'd recommend writing down in Spanish a few key phrases you think you might need to get around.
3) Take a taxi to Miraflores and just wonder around. The same for downtown Lima. It will be safe. Just don't carry a lot of money in your wallet. Leave your passport in the hotel's safe, and carry your DL as an ID. Remember that data usage can be very expensive, so don't rely on getting maps from your IPhone unless you have preloaded them.

If you are more adventurous, find a way to go to the ruins of Pachacamac. It is an hour away from the Sheraton and although not nearly as impressive as the ruins in Cuzco, it is still worth the trip to go see them.

Have fun!