Salem sits in a rain shadow and is drier than the Tamil Nadu coast. The best time to visit is October to February, when temperatures are in the mid-20s and the air is clear. The city gets some rain in the northeast monsoon (October–December) but nothing like the amounts on the coast.
March to June is hot — temperatures can reach 40°C and the city loses its appeal rapidly. The Yercaud hills stay 8–10°C cooler year-round, which is why they exist as a hill station in the first place. If you are heading up there, October to March is ideal; avoid April–May when Yercaud gets crowded with heat refugees from the plains.
The Yercaud Summer Festival, held each year in late April or May on the hilltop, includes flower shows, boat races on the lake, and cultural programmes. It draws large crowds, so accommodation books up early if you want to coincide with it.