American Samoa is hot and humid year-round. Temperatures stay between 27–32°C (80–90°F) and don't vary much by season. Humidity is high throughout. What does shift is the rainfall.
The dry season runs from May to October. This is the cooler, sunnier stretch, and the most comfortable time to hike. Trade winds bring some relief from the heat. September is typically the driest month. This is also prime surfing season, with consistent south swells hitting the island's reef breaks.
The wet season runs from November to April. Rain can be heavy and persistent, and cyclones are possible between December and March. That said, the sea is calmer and clearer in these months — if you're coming primarily to snorkel, December through April can actually be ideal, especially around Ofu's reef.
June through August is peak season for American visitors, school holidays aligning with the Pacific dry season. If you prefer fewer people — and "fewer" here means very few — the shoulder months of May or October are a good choice. In September and October, humpback whales pass through the waters around the islands.
There is no truly bad time to visit. The rainforest is always green, the reef is always there, and even in the wet season, rain often comes in short sharp bursts rather than all-day downpours.