I was in Lima, Cusco and Machu Picchu about 2 years ago and loved every minute. My favorite restaurants in Lima are Il Postino
http://webserver.rcp.net.pe/ilpostino/
which has great Italian food.
La Rosa Nautica is a famous place and the food is great there too. It is a typical kind of tourist place though.
http://www.larosanautica.com/rn_quienes_en.html
And for dessert try
http://http://www.pasteleriasanantonio.com/ We went there every possible day we could!
For traditional Peruvian dishes I liked
http://http://www.pasteleriasanantonio.com/
Have a great time! I'm hoping to take my 14 year old son in the spring.