Generally, the best season to spot whales (ballenas jorobanas) in North of Peru is the winter months, from late August to early November.
The region of Piura has a great variety of marine fauna, and apart from whales you can also see -if lucky- dolphins, sea lions, turtles, pelicans and other kinds of birds. In fact, the area is a crossing poing of two underwater currents: the hot current El Niño and the cold current Humboldt, which explains the richness of species in the region.
There are tour operators in Máncora who can take you to a boat trip to observe whales. We asked about the prices, and they were around 200 nuevos soles, approximately 80 USD.
While still pondering what would be the chances to actually see the whales on a boat tour we took a stroll at the beach...