October to March is the best window: warm dry days, cool nights, no rain. April and May are hot and humid but still passable. The monsoon (June to September) is heavy and floods are common — rural day trips become difficult, but the river is at its most dramatic.
The Ambubachi Mela in late June is the big event of the year — a four-day festival at Kamakhya marking the goddess's annual menstruation, drawing several million pilgrims. The city is mobbed, hotels are full, and the temple is closed for the first three days. Avoid these dates unless you want to be part of it. Bihu falls three times a year (April, October, January); the spring one (Bohag Bihu, mid-April) is the biggest and a good cultural time to visit.