The best time to visit the Central Peruvian Andes is between May and September. During this period there is consistently dry weather and storms are less frequent than in other comparably sized ranges in other parts of the world. There is less rain and all the peaks in the Cordillera Blanca can be attempted during this time. Naturally, this is also the high tourism season for the entire country so you will encounter much traffic.
Many of the lower peaks in the region can be climbed during the rest of the year, but the weather is both less predictable and less desirable. During June, Huaraz hosts the Semana del Andinismo, a world-renowned festival to celebrate all things to do with the surrounding mountains. You can see and experience the town in full-swing, celebrating the life force of the Andes. It will also be the busiest time so make sure to book ahead.