The idea of island hopping seems to be twofold: 1) Avoid costly battles where the enemy is strongest, and 2) Take only the islands that are necessary/suitable for continued advance. I have a couple questions about this. First, doesn't this strategy hinge on some level of naval superiority? Otherwise, if we just have an array of alternating strongholds, it's not clear that we've accomplished anything. Our somewhat isolated victories could be just as susceptible to "withering on the vine" as theirs.
Second, what was the selection criteria for "necessary/suitable for continued advance"? I'm guessing that it's some combination of "can house people" and "can support airstrip(s)", but what other factors would go into determining which islands were necessary to take and which could be leapfrogged?
While you wait for a more targeted answer, you might be interested in some previous threads on island hopping in the Pacific Theater of World War II:
The Theory and Practice of Island Hopping
What alternatives to the Pacific Island-Hopping Campaign were put forth by American military planners during the Second World War? - 7 comments, over 1 year old.
This thread delves into the theory surrounding "island hopping" and its competition in the early 20th century and what prompted its selection in World War II.
Why did more Japanese soldier die during America's Island Hopping? - 6 comments, over 10 months old.
This thread details the effects of the almost complete firepower, air power, and naval power superiority that the US brought to bear in its island hopping had on the fortified Japanese positions.
Did the recapture of the Philippines by MacArthur serve any use in the overall picture of the Pacific Campaign, besides the obvious propaganda purposes? - 28 comments, over 2 years old.
This goes into the sequence of events and some of the necessity of the Philippines campaign, but is far from a complete exploration of the matter.
Counterfactuals and Alternatives
Why did the U.S. engage in a strategy of island hopping in the Pacific during World War II - as opposed to simply blockading the Island of Japan? - 6 comments, over 1 year old.
A variety of flaired users talk about the (im)practicality of such a long ranged campaign so deep inside enemy territory and also talk about the actual submarine blockade conducted by the United States in the final portion of the Pacific War.
Why did the US spend so many resources attacking small islands during WWII? In other words, why didn't they just go straight for the Home Islands? - 43 comments, over 2 months old.
This goes into the political, logistical, and military factors that restricted US action during the war as well as the defensive strategy adopted by the Japanese after their initial expansion in the Pacific.
Why did the US wage the war in the pacific by attack the islands occupied by Japan instead of attacking them through China? - 5 comments, over 1 month old.
This thread addresses the logistics of US operations in China as well as the events that occurred throughout the war that made island hopping and the Philippines assault to be the most preferable option once it was available.
Other Threads About the Pacific Theater
Compared to the American 'Island Hopping' campaign, how important was the British/Commonwealth battle for Burma or the ongoing Chinese war against the Japanese? - 4 comments, over 1 year old.
The commenters compare the goals, scale, resources, possible outcomes, and results of both campaigns to arrive at which was of more major import to the war as a whole.
How did the local Pacific Islanders feel about WWII? - 6 comments, over 1 year old.
This thread goes into the treatment of Papua New Guinea natives by both Allied and Axis forces, with particular emphasis on the Australian side.
How did isolated Pacific Islander populations react to seeing the planes and ships of World War II? - 14 comments, over 1 year old.
Commenters here go into the longer term effects of the war on native peoples in the Pacific as well as the actual state of contact and knowledge prevalent throughout the islands.
The linked answers have all the info pretty much. But in short you are looking at it from the wrong way.
The way the US planned to defeat Japan was THROUGH Naval Superiority.
War Plan Orange(the plan to operate against Japan) was based on getting the Pacific Fleet into Japanese home waters in good condition, with bases nearby, and able to win a decisive fleet action and then move to blockade the islands.
The options then were to rush with everything to Guam and then the Philippines and hope they had enough strength, and bases left to prepare for battle once there (as it would take a few weeks for the fleet to gather and the reserves to join). This however played to Japanese home field advantage by allowing them to wear down the USN as they charged West or were caught escorting convoys in hostile waters and fight on their terms.
The better option then was to leave Guam and the Philippines to their own devices, while the Fleet gathered at Hawaii (or California before that) then took bases as they moved West significant study wad given to what islands had sufficient lagoons for fleets to gather and ready themselves, in addition to area for shore facilities. The Marshalls, Caroline, and Marianas had several options. With Truk Lagoon being one of the finest natural harbors in the world, eventually becoming the primary forward base of the IJN.
Thus once forward bases were seized the fleet could relieve the Philippines, and once rested confront the IJN with a strong chance of success.
The rise of the air plane then did not fundamentally change this strategy, as WW2 went on to show.
One of the reasons the US spent so much time developing Subs and carriers between the wars was to give the Pacific fleet the ability to forward project in front of their advance bases, and make themselves a menace to the IJN before the battle fleet could come up. Long range and high speed were key elements in USN submarines so that they could serve as fleet boats helping the main body, and surge ahead and catch enemy fleets, as well as begin the blockade on their own(and they ended up being VERY successful). Aircraft also allowed for better patrolling on the lines between the islands, reducing the significant needs in earlier plans for escorts to fend off the Japanese Battle Cruisers(later reconstructed), and later cruiser force making fast strikes on supply lines in attempts to both disrupt the build up and draw off elements of the battle fleet.
War Plan Orange: The U.S. Strategy to Defeat Japan, 1897-1945 by Edward S. Miller