October to March is the best time to visit Deoghar for a comfortable trip. The weather is mild and dry, temple queues are manageable, and the surrounding hills are pleasant to explore.
If your purpose is the Shravani Mela specifically, that falls in the month of Shravan (July–August) — an extraordinary experience, but a completely different kind of visit. Expect very large crowds, long waits, heavy rain, and accommodation booked out well in advance. In 2026 the Mela runs from 30 July to 28 August.
Mahashivratri (February–March) is the other major peak. Crowds are significant but nothing on the scale of Shravan, and the weather is far more forgiving.
Avoid April to June if you can. The heat is punishing for the amount of standing and walking a temple visit involves.
For a quieter darshan at any time of year, weekday mornings are considerably easier than weekends.