Puno is another climate with an extreme temperature swing in the winter. Average in July is +18/-6C (64/21F), similar to Juilaca. I wouldn't want to live in either place but it would be interesting to visit.
Of the original choices,
I vote for Cusco. It doesn't get a warm summer, but it's comfortable year round. Most of the climates don't get enough rain.
I'd take Chachapoyas instead of Cusco if it was a choice. Huánuco has warm days year-round but I don't think 350mm/14" is enough precipitation.
Current stats:
Cusco-6
Iquitos-5
Ica-3
Arequipa-1
Piura-1
Trujillo-1