Map from Google - Marshall_Islands

In the Marshall Islands, the climate is tropical, hot all year round, with little variation in temperature throughout the year, and maxima around 86 °F. The trade winds blow constantly, tempering the heat. In the capital, Majuro, the temperature is definitely stable throughout the year: the minimum temperature is around 77 °F, while the maximum temperature is around 86 °F; it rarely drops below 72 °F at night or exceeds 90/91 °F during the day.
Here are the average temperatures of Majuro.
Average temperatures - Majuro
MajuroJanFebMarAprMayJunJulAugSepOctNovDec
MajuroJFMAMJJASOND
Min (°F)777777777777777777777777
Max (°F)868686868686868686868686

The islands are divided into two groups arranged from north to south, called Ralik and Ratak, but the main difference in the climate of the islands lies in the rainfall and depends on latitude: the central and southern islands are rainy all year round, so that their climate can be called equatorial, while in the islands lying north of the tenth parallel (Enewetak, Bikini, Rongelap, Taka, Utirik, Taongi), there is a relatively dry season from December to April. In the this northern group, the annual precipitation is around 60 inches, with a maximum between August and October, when it exceeds 8/10 inches per month, and a minimum from January to March, when it drops below 1.6 inches per month. During the years of La Niña, when the rains decrease throughout the islands, these northern atolls, which are already less rainy in normal years, can experience drought.
Here is the average precipitation in Enewetak.
Average precipitation - Enewetak
EnewetakJanFebMarAprMayJunJulAugSepOctNovDecYear
EnewetakJFMAMJJASONDY
Prec. (in)1.211.62.24.54.17.37.77.99.86.12.655.5
Days131012131718222121222016205

Moving south, rainfall becomes progressively more abundant, so that the it can reach 100 inches per year already in the atoll of Kwajalein. At this latitude, between January and March the rains are still acceptable, since less than 4.3 inches per month fall.
In the southernmost atolls, the rains are really abundant: in the capital Majuro, 132 in of rain per year fall, with a minimum of 7 inches in February, and a maximum of 14 inches in October. Here is the average precipitation in Majuro.
Average precipitation - Majuro
MajuroJanFebMarAprMayJunJulAugSepOctNovDecYear
MajuroJFMAMJJASONDY
Prec. (in)8.17.18.310.61111.412.211.412.614.213.411.6132.1
Days181618202324242323242322258

The amount of sunshine in the Marshall Islands is always at least acceptable, because even in the wettest months the rains do not last long, given that they occur in the form of short and intense downpour or thunderstorm.
The Marshall Islands can be affected by tropical cyclones during the period from June to November. In particular, in this area, many of the typhoons which then head towards south-east Asia are formed: this means that generally they do not affect these islands at the peak of their strength, because they are still in the early stages.

Majuro

The sea in the Marshall Islands is pleasantly warm all year round, as we can see in the following table.
Sea temperature - Majuro
MajuroJanFebMarAprMayJunJulAugSepOctNovDec
MajuroJFMAMJJASOND
Sea (°F)848282848484848484848484

When to go

The best time to visit the Marshall Islands runs from January to March in the central and southern atolls, because it is the least rainy period, even though there is no shortage of showers and thunderstorms, while in the northern islands it runs from December to April, being a period of quite rare and generally not abundant rains.

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.
For the reef, equipment for snorkeling, water shoes or rubber soled shoes.