They want bases to strengthen the military attacks leading up to the main land of Japan. They also wanted to weaken the Japan's troops which were based on those islands. The reason they started with the Solomon Islands is that it would take a while for Japan to mobilize their troops to get to the Solomon Islands. It was also a major advantage point for the American troops to use as a naval base, or a air base I forget which, but it was a good idea at the time.
