Let me detail you some of the food you can find here.

 1. Cuy Chactado (Guinea Pig): You can find this dish mostly in the Mountainous Area (Sierra) or in restaurants in Lima City but is not the same. The taste is really singular because the guinea pig meat is tough.
 2. Ceviche: It's raw fish mixed with lemon juice, pepper salt; it is delicious. Be careful some restaurants prepare this dish with a lot of "Aji" (Something like a Chili pepper)
 3. Pachamanca: I think this is what you meant when you said Cozido das Furnas, it is an ancient dish made to honor the Pachamama (Mother Earth). People dig a hole in the earth and then put rocks in it and get heated with wood, on it they put the seasoned meat (Chicken, Pig,  Beef), then is served with potatoes and Favah Beans. I totally recommend this it is one of our best dishes.
 4. Juanes: Is a dish from the jungle, it is made of rice, chicken meat, egg and then it is boiled inside a leaf called bijao that it gives the rice a green color. It is delicious.

And i could go on with many dishes like carapulcra, rocoto relleno, caldo de cabeza, papa a la huancaina, seco de cabrito, etc.

if you want to try most of these dishes at once you should ask in the hotel reception for where you can find a "Buffet Criollo". If i can suggest you a site there is a restaurant in Larcomar in front of the Marriot Hotel.

Restaurants: (I will add more later...)

- Vivaldi
- Rustica
- La Bonnbonniere

Note: As for drinks i strongly suggest Pisco Sour.  Don't get too many this drink is really tricky you can get drunk really fast ;)