I live in Peru and I'm from the US. The food is great here and cheap. I don't recommend the city of Lima, way over populated but I do recommend anywhere else out side of Lima like Cusco or the Amazones.
I have traveled to all 3, but personally i enjoyed Peru more. The food was the best even the drinks. china, japan, russian, italian, and afro food is inspired in peruvian cuisine, amazing! they have machu picchu, the amazon, the nazca lines, the inca trail, and other really pretty sites!
I was studying abroad when i was in college and went to these fantastic countries. but all my college friends and i agree that peru was more fun because the vibe was young there, plus there was more too see than just pretty buildings and museums.
There are good things to see in all of those countries.
Argentina is priettier.
Peru has jungle and the most interesting archaeology. Argentina has Buenos Aires and Iguazu(sp.) Falls. My vote is for Peru, unless you like big cities.