The best time to visit Allahabad for ordinary tourism is October to March, when the temperature is manageable (cool mornings, warm days) and the light is clear. This is also the period of the Magh Mela — held annually in January and February at the Sangam — which is a remarkable spectacle even in non-Kumbh years.
The Kumbh Mela occurs every twelve years (the next full Kumbh after 2019 is in 2031); the Ardh (half) Kumbh every six years. These are transformative events that dwarf normal tourism — if you want to witness one of the great human gatherings on earth, time your visit accordingly, but be prepared for extreme crowds, elevated prices, and infrastructure under strain.
Summer (April to June) is brutally hot; the monsoon (July to September) brings flooding around the Sangam and makes access to some ghats difficult. Avoid these periods unless the Kumbh Mela specifically draws you in.