Map from Google - American_Samoa

At American Samoa, archipelago in the Pacific Ocean located south of the Equator, the climate is hot, humid and rainy throughout the year, with a maximum in rainfall from December to March, and a relative minimum from June to September.
The temperatures are stable, and vary little between the hottest period (December to April), when highs are about 88 °F, and the coolest period (June to August) when they are around 84 °F. The night temperatures are almost always above 68 °F. The trade winds blow steadily throughout the year, especially from May to October, and blow stronger during the day, making the heat more bearable.
Here are the average temperatures of Pago Pago.
Average temperatures - Pago Pago
Pago PagoJanFebMarAprMayJunJulAugSepOctNovDec
Pago PagoJFMAMJJASOND
Min (°F)777777777777777777777777
Max (°F)888888888684848486868688

The rains fall in the form of downpour or thunderstorm, and they are intense but they generally don't last long, so that the sun shines frequently and regularly, even in the rainiest months. From December to March, however, sometimes the rains may last for the whole day.
Rainfall is enhanced by the slopes that are found in the volcanic islands (Tutuila, Ta'u, Ofu and Olosega), which therefore are wetter, while in the small islands and the flat atolls (Aunu'u, Swains and Rose), about 100 inches of rain per year fall. In the volcanic islands, the rainfall amount vary depending on slope exposure, so that it goes from about 120 inches per year along the sheltered coasts, to 160 inches per year in the coasts exposed to the trade winds; in hilly and mountainous areas it can exceed even 200 inches per year.
In the capital, Pago Pago, located in Tutuila Island, 122 inches of rain per year fall, with a maximum of around 14.5 inches in December and January, and a minimum of 5.9/6.3 inches between June and August. Here is the average precipitation.
Average precipitation - Pago Pago
Pago PagoJanFebMarAprMayJunJulAugSepOctNovDecYear
Pago PagoJFMAMJJASONDY
Prec. (in)14.412.611.61110.65.96.56.37.710.411.214.6122.8
Days242124222018191818212123249

American Samoa is exposed to the Southern Hemisphere tropical cyclones, which occur from November to mid-May, although they are more likely from December to March.

Pago Pago

For swimming, the sea is warm all year round, as you can see in the following table.
Sea temperature - Pago Pago
Pago PagoJanFebMarAprMayJunJulAugSepOctNovDec
Pago PagoJFMAMJJASOND
Sea (°F)848484848482828181828284

When to go

The best time to travel to American Samoa runs from June to September, being the less warm and rainy; anyway, even in this period some downpour or thunderstorm must be put into account.

What to pack

All year round, tropics-friendly, loose fitting clothing, sun hat, a scarf for the breeze, a light sweatshirt for the evening, light raincoat or umbrella.