From the little reading I've done, it seems we had some bases up there(notably Dutch Harbor), why didn't we use them to attack and harass the northern home islands, or maybe even invade Japan or Manchuria?
Geography would probably be a challenge, but I wouldn't think of it any more a challenge than a sandy atoll with nothing on it, and we already owned them negating the need for an invasion(of the Aleutians).
The American did use the Aleutians to attack Japan after the conclusion of the Aleutian campaign. The Japanese seizure of Attu and Kiska ironically created the very American build-up in Alaska that the Japanese feared. While some American thinkers, most notably Alfred Thayer Mahan, did hypothesize a northern route against Japan in the early twentieth century, there was little in they way of a robust military infrastructure in the Alaskan theater at Pearl Harbor. The war and the Japanese occupation changed that and the Americans did use air bases in the Aleutians to attack the Kuriles and Hokkaido. These attacks though achieved very little.
One of the chief reasons why the northern Pacific option was not expanded upon was geography. Northern Pacific weather provided only a brief campaigning season and added more demands on ships' and planes' normal tempo of operations. Visibility in the region is poor at the best of times and the extreme winter temperatures would have precluded truly mass operations. The Aleutians campaign had shown that the region was tough on equipment. The area was also not nearly as familiar an area as the Central Pacific, or even the SW Pacific to American planners. The famous "Battle of the Pips", where a USN task force engaged with radar echoes because of poor visibility was only the most famous example where the fog of war made this a difficult region to conduct modern operations.
American planners did envision a strategic bombing campaign against northern Japan and the Kuriles from the Aleutians. Although the USN and 11th Air Force did conduct air raids against northern Japan from mid-1943, these bombing missions were difficult, and not just because of Japanese resistance. Weather conditions caused a large number of bombers to abort and range limitations of the bombers meant that there were few truly worthy targets for American air power.
In the end, while some Americans played with the idea of a northern attack route, this was not a viable option. Unlike the Central Pacific, which the USN had been wargaming for the better part of thirty years, the northern Pacific was a relative unknown quantity. Some planners in the 1900s and 10s did speculate on the possibility of a northern drive. Mahan may have dismissed weather concerns with the idea that "white men thrive in the cold," but he was somewhat alone in the upper echelons of the USN. Most of the prewar development of this region was defensive in nature, seeking to prevent the Japanese from seizing it rather than as a springboard for an attack on Japan.The experience of difficulties encountered during the Aleutian campaign further dampened any enthusiasm for the northern alternative. Weather, distances, shortages of ice-free harbors, and the lack of preexisting infrastructure meant Alaska was not a propitious area which to launch a major military campaign.