I was taught in school that the Pacific theatre was essentially a separate war (fighting with Japan both started before the invasion of Europe and ended after Nazi defeat, the US was more or less the only Allied power in the theatre, etc.), that no unconditional surrender from Japan was on the table so fighting would continue, and the path to victory, according to people like General Douglas MacArthur, was a land invasion. I was also taught that this line of thinking was a major justification for using nuclear weapons - the loss that would occur from a land invasion was calculated to outweigh the loss from dropping nukes. Is this incorrect? Was there any other proposals for ending the War with Japan under the circumstances? Was it truly a binary choice: invasion or nukes? I would also like to note I understand the other intended consequences of dropping the nukes besides ending the war such as intimidating the Soviet Union.
No, there was no calculation during the war of "bomb or invade" -- this was an invention of the postwar period to retroactively justify dropping the bombs. This section of our FAQ has plenty of interest for you, but I would highlight these threads in particular:
To specifically address some of the misconceptions in your post:
The U.S. did have logistical support from various allies during the war -- although the initial ABDA (American, British, Dutch, Australian) combined forces were defeated fairly quickly when the Japanese breached the Maylay barrier, the U.S. relied on bases in Australia to operate against Japan, and the British Pacific Fleet played an unglamorous but important role on strikes on outlying islands and eventually the Home Islands starting in 1944.
There were plans for a land invasion of Japan, but there was no question of bomb or invade -- atomic scientists were studying things like whether bombs could be used on invasion beaches and so forth (what we'd consider to be "tactical" uses of nuclear weapons today).
The bombings didn't happen in a vacuum -- by the time of the strikes on Hiroshima and Nagasaki, the U.S. had already destroyed close to 70 Japanese cities by firebombing, including large portions of Tokyo. (Hiroshima and Nagasaki were actually on a "reserved" list of targets not to firebomb, so that scientists and planners could study the effects of the atomic bombs.)
Truman never made a positive decision to use the bombs -- he learned about them upon becoming president, and went along with plans to use them, but the narrative where he struggles with a "bomb or not" decision is wrong. He made a positive decision to stop bombings without his approval after Nagasaki; he may or may not have known that Hiroshima was a city before it was bombed, but he felt uneasy about civilian deaths in Nagasaki.
And finally, it's not clear whether the bombs themselves or the Soviet invasion of Manchuria, or both, or other factors, were what finally drove Japan to surrender -- reasonable people can disagree on this.