I have cebiche, cuy, alpaca, and pisco sours on my list of foods in Peru that I have to try. Other recommendations for "can't miss" foods, snacks, and drinks in Peru? My only limitations are: (1) I can't risk getting ill, and (2) I don't do offal (i.e., no beef hearts)

I think you might be surprised that the anticuchos are really good. Beef heart tastes like steak, no organ-y taste. It has to be thinly sliced or can be a bit tough. Surprisingly Pardos does it well. The pollo a la brasa (Los Toldos in Cusco is good). The soups in the highlands, quinoa soup is good if you are feeling off from altitude and dont want a big meal. Real chicha morada (not the bottled kind). If you are lucky to find a cart with mazamorra morada or arroz zambito (not typical in restaurants).

Lucuma ice cream. (And maracuya). 4D has the best ( there is one at the airport). Picarones Mary cart in Park Kennedy Lima. Churros San Francisco near the Plaza de Armas (I think on Jiron Lampna). Causas (pureed yellow potato with lots of choices if filllings). Desserts with dulce de leche are popular.
Stews made with cabrito (kid) or seco de cordero (lamb).

Of course lomo saltado is virtually the national dish but not my favorite.

In the Sacred Valley, look for Chicharrones in the small towns just outside of Cusco. It's fried pork. Super delicious. I'll second Los Toldos for the pollo a la brasa and definitely get chicha morada. And stop by a local's house for chicha (corn beer). It's not brewed in bulk, so you have to look for the plastic "flags" flown at houses of people who brew it. About 1 sole for a giant cup. (But don't drink it all!)

Thanks so much to both of you. The ice cream and chicharrones are definitely on the list. The local's home brewed corn beer, on the other hand...

I'm with you on that...

Mmmmmmm Churros.