Lt JG John F Kennedy took command of PT-109 on Tulagi on April 23, 1943. They moved to the Russell Islands on May 30, 1943 in preparation for the invasion of New Georgia.
After more than a year of fighting on the bigger island, Henderson Field, the target of the initial invasion which had been started by the Japanese, had grown to the point that it dwarfed anything available on Tulagi.
And thus, the colonial capital (and eventual capital of the Solomons) was moved to Guadalcanal not long after hostilities had ended.
Incidentally, the much smaller size of Tulagi also meant that ocean breezes could reach all parts of the island, making it more resistant to tropical diseases and a more appropriate location for the colonial capital in the beginning.