Perry I'm familiar with some of the cities you mention in Peru, except for Tarapoto?
The only city worth mentioning is Arequipa..! Still comparing it with BA is like comparing Paris to Nice ..? (Nice is a great place)
In BA we have Calle Corrientes with all the Culture , Teatro Colon, Connectivity Arequipa is off the main flight lines. Restos here are international, Peruvian food is great but not very varied. Graduate Education in Arequipa ? Public Health in Arequipa..? Maybe housing is cheaper in Arequipa.
Still Arequipa compares well with other smaller cities in Argentina, where everything is cheaper but you don't have the Metropolitan cultural content. Maybe San Rafael, Mendoza