The best time to visit Sri Lanka is two different answers
Sri Lanka has two monsoons hitting opposite coasts at opposite times, so there is no single best month — there is a best month for where you are going.

Almost every article on this question gives you one answer. That answer is wrong, because the island runs two separate monsoons.
The two monsoons
The Yala monsoon brings rain to the west and south coasts and the central highlands from roughly May to September. The Maha monsoon brings rain to the east and north from roughly October to January.
They do not cancel out. They mean that on any given date, somewhere in Sri Lanka is dry.
So, practically
December to March is the sweet spot for the classic circuit — Colombo, the Cultural Triangle, the hill country, and the south coast. Dry, and the whale season off Mirissa runs December to April. It is also the most expensive and most crowded window, and you should book accommodation well ahead over Christmas and New Year.
April is transitional and quietly excellent. Sinhala and Tamil New Year mid-month means some closures and a lot of domestic travel, but the weather holds on the south coast and the crowds thin after the first week.
May to September is the time to go east. Trincomalee, Arugam Bay and Nilaveli are at their best exactly when the west coast is being rained on. Arugam Bay’s surf season runs May to October.
October and November are the worst months overall. Both monsoons are transitioning and you can get rain anywhere. If these are your only dates, go anyway — it rains hard for an hour and then stops — but expect Horton Plains to be clouded in.
The part nobody mentions
Rain in Sri Lanka is mostly an afternoon event, not an all-day one, and the hill country is beautiful in mist. The months to actually avoid are not the wet ones; they are the ones where your specific route is wet. Tell us your dates before you fix them and we will tell you which direction to go round the island.
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