Shorter answer: Japanese construction of an airfield on Guadalcanal was the immediate cause of the Solomon Islands campaign. The airstrip was renamed Henderson Field after Americans invaded and captured it in 1942, but was originally built as a base for Japanese operations. This base would have hampered Allied operations throughout the Pacific.

Imagine a series of concentric rings with Guadalcanal at the center. The largest of the rings would have a radius of about 2,000 miles, representing the maximum scouting range of the Kawanishi H8K "Emily" seaplane. The H8K's predecessor, the H6K "Mavis," had a somewhat shorter but still substantial range. The seaplanes could be used for long-range patrols to sight enemy shipping and make life difficult for any submarines spotted.

An aside: Japan's seaplane base in the Eastern Solomons was actually at Tulagi, just a few miles north of Guadalcanal, but you get the picture.

Within that larger circle is a circle representing the maximum combat radius of Japan's land-based long-range bombers. The Mitsubishi G4M "Betty," the finest Japanese bomber in the theater, could carry a torpedo or bomb load about 1,000 miles out. This radius encompasses Vanuatu and the entirety of the New Hebrides and also extends far enough south to envelop New Caledonia. These islands were controlled by the Allies and important bases during the Solomons campaign, and would have been threatened by a Japanese air force at Guadalcanal. Smaller than the long-range bomber radius would have been the range of Japanese fighter aircraft and smaller land-based bombers. These aircraft generally could have reached Vanuatu but not New Caledonia. They also could have projected their power out over most of the Coral Sea and several hundred miles east of Guadalcanal, interdicting any naval forces in the area and attacking ships carrying supplies. In a worst-case scenario, Japanese land-based bombers and fighters could be used to protect an invasion force of the New Hebrides, which would then bring New Caledonia into even greater danger. Japan's protective perimeter would have expanded further outward, with new concentric circles emanating from the newly-acquired bases.

More immediately, however, Japanese land-based aircraft posed a threat to the supply lines to Allied bases in the New Hebrides. Invasion of Australia was no longer a threat following the Battle of the Coral Sea, but there were still concerns about keeping sea lanes open to the allies in New Zealand and Australia. These are sometimes called "sea lines of communication," or SLOCs. In addition to the military forces of Australia and New Zealand themselves (which made a significant contribution to the war), there were tens of thousands of American forces in Australia by 1942, and that number grew as the war went on. It was vital to be able to be able to provide the resources necessary to maintain that fighting force and support their operations. Japanese aircraft on Guadalcanal would have made it difficult to keep these forces resupplied; Japanese expansion to Vanuatu or New Caledonia could have been disastrous and threatened to cut off Australia almost entirely.

Why not attack Hong Kong or Singapore or Malaysia? There are two major reasons why.

The first is that the same concepts just discussed -- sea lines of communication and concentric circles radiating aircraft -- applied elsewhere as well. Sailing an fleet of warships and amphibious forces to any of those locations would have brought them under attack from Japanese aircraft around the Pacific and the Japanese navy. Each place you mentioned was comfortably within Japan's empire by 1942. Attempting to invade within it would have been met with defeat. Even if you could somehow, hypothetically, defeat Japanese naval and air forces somewhere like Hong Kong, you would have still had to preserve enough of your invasion forces to win a battle. And after that, you'd have to be able to provide supplies and reinforcements, or they'd eventually be defeated through attrition and counterattacks.

More practically, there were no resources to target other locations. Any account of the invasion of Guadalcanal will mention that it was ruefully nicknamed "Operation Shoestring" during the planning phases. The Allied joint chiefs had made the strategic decision to prioritize the European theater while holding off the Japanese advances in the Pacific. The joint chiefs agreed broadly that Europe should receive the lion's share of materiel, but there was still significant infighting about resources for the Pacific and what it meant to hold off the Japanese advance. On the one hand, invading Guadalcanal would prevent the Japanese from threatening to expand elsewhere in the south Pacific; on the other, it was clearly an offensive action to seize Japanese territory. The United States was not fully mobilized by mid-1942. It was only growing stronger, but was still a long way removed from the wartime economy of 1944 and 1945 that most people remember.

The invasion of Guadalcanal (plus Tulagi and Gavutu) went forward with a relatively small force: Just two Marine divisions landed initially. They were short on supplies and the Navy was short on ships to protect the invasion force. The landings were successful due in no small part because they caught the Japanese entirely by surprise. Things got dicey pretty quick, however, because even the limited supplies for the operation weren't fully unloaded before the Navy withdrew, leaving both the Marine invaders and the Japanese garrison mostly cut off for weeks. Attempting a similar operation deeper within Japan's 1942 holdings would have been disastrous.

American commanders in the Pacific eventually realized that the fighting in the Solomons could and would be decisive. Once it became clear the Marines (and Army reinforcements) would hold the island, the Americans turned the Solomons into an attrition campaign. Unlike some later operations in the Pacific where the Allies had the clear upper hand, the Solomons was a brutal effort fought often on equal terms. It was a maelstrom that sucked in men, ships, and planes from both sides. The Allies were willing to make this trade because it bought them time. The Japanese economy was already more or less operating at full capacity by 1942; the American industrial base was just revving up. The Americans would be able to replace losses in the Solomons with ease in coming years, while Japan never recovered. The Battle of Midway is often remembered as the turning point in the Pacific because it halted Japanese offensive operations, but the Solomons campaign was no less decisive. By the end of the Solomons campaign in 1943, the Allies were prepared to go on the offensive in the Pacific while the Japanese had expended dozens of warships, hundreds of aircraft, and tens of thousands of men that were irreplaceable. After the fighting in the Solomons, the Japanese would never be able to fight the Allies on truly equal terms again.