Anything with the giant corn native to Peru is usually great. So are the many potato dishes. Peru grows some of the tastiest potatoes. One dish that shows off the potato best is Papa Rellena, (mashed potatoes, stuffed and deep fried. fillings range from meat, eggs, veggies and olives). The best comparison to Papa Rellena that we have in the USA is probably a Knish. Another thing to try is Yuca. Yuca that is fried is a great alternative to potatoes, if you have a choice.
Chicha Morada is the drink to have especially when it's made with fresh (not canned) pineapple. Chicha is made from purple corn, and tastes similar to fruit punch.
You should also try their national soda, Inka Kola. Some people think Inka kola is too sweet, and it does taste a bit like bubble gum. But Peru is very proud of this soft drink, so you should give it a try at least once.
Since you do eat beef, Anticucho is a must. While you can now commonly find them made from any meat, such as chicken. The traditional Anticucho is made from beef heart. Also Lomo Saltado is found everywhere, in Peru. Commonly made with beef, although I've had it made with chicken and shrimp. Lomo Saltado is tomatoes, onions, garlic, peppers, with vinegar and soy sauce, Sauteéd with French Fries, and served with rice.
For seafood, Peru is famous for Ceviche. But I prefer the lesser known Tiradito (much like Ceviche, but with a milder flavour) which highlights ginger instead of onions as the flavour base.
If you're feeling a bit adventurous, Mondongo Ayacuchano ( Beef Tripe Stew) would be one dish to seek out. The best comparison we have here in the USA to Mondongo Ayacuchano is Menudo.