I will try to answer a little bit here. The US had a plan, Operation Downfall, to invade the Japanese home Islands. Specifically they would have first invaded Kyushu (Operation Olympic) before invading Honshu. (Operation Coronet). Operation Olympic was going to secure a large foothold on home islands (securing about a third of kyushu) in order to support the larger and more essential Coronet via supply base and air support. Operation Coronet would have landed near Tokyo and driven to capture the capital quickly. Altogether Downfall was planned to be the largest amphibious assault in history with just shy of about 2 million military personnel involved.

Ultimately however, due to the geographical limitations, the landing spots were obvious to the Japanese who developed Operation Ketsugo to try and repel the American assault. They massed forces in the appropriate spots to repel the invaders (including arming and giving very crude training to civilians) and prepared what was left of the navy to provide anti air fire while docked (they did not have the fuel to leave, and would not last long anyway as most ships were damaged). They also intended to use a large number of kamikaze planes. Altogether more than 3 million military personnel and more than 25 million civilians were to have some role the defense of Japan (mostly logistical, but some were given crude weapons like spears and told killing even just one American soldier would be sufficient).

If the Japanese hadn't surrendered it was likely Operation Downfall would have commenced, in which case it was likely that a relatively small number of atomic weapons would have been deployed to support the landings and fighting. I have seen sources range from 7 to 15 bombs would have been available over the course of the estimated duration of operation. My understanding is that these would have been used for cities or other areas where the Japanese were heavily fortified in order to save the strength of the American soldiers. Side note: that the real world impact of radioactive fallout did not seem to be fully considered or understood by those making the plans and many American troops would have faced significant levels of exposure. For instance guidelines stipulated Americans should avoid the blast area for around 48 hours before moving into the area. The resulting radiation exposure would have added in a more long term casualty element beyond the already sure to be high immediate cost in life as well.

Of course all of this is ignoring the role of the Soviets. The Japanese had actually held out some hope they might be able to approach the Soviets to negotiate a more equal peace with the Allies, but the Soviets rebuffed these advances. They were finishing up in Europe and now the Cold War was starting in earnest and both the USA and the Soviets were rushing to have as much influence as possible, and the Soviets would have loved to either control Japan similarly to Eastern Europe or at least have some form of split in order to have a larger influence in Asia, while America wanted to deny the Soviets this. In fact not only were the bombs an attempt to avoid the bloody cost of Operation Downfall, they were also an attempt to shut the Soviets out of the peace process with Japan. Once we dropped them the Soviets rushed to invade Manchuria and would have quickly developed their own invasion plan of Japan in an attempt to get in on this process.

Now, on a slight tangent and this is more of a debate, but it is argued the soviet invasion is what triggered the Japanese surrender rather than the bombs. The military high command was split 50/50 on whether to surrender or keep fighting and the emperor made the final decision. This is speculation on my part, but I would say he and the other Japanese officials felt life would be better under the USA than the Soviets, and may have made some educated guesses based on how the peace in Europe was starting to develop. The whole soviet ideology was not compatible with a "divine monarch" where as the Americans, desperate to keep the Soviets locked out of Japan might be willing to make concessions to keep the Soviets out (which is more or less what happened given the continued reign of the emperor and lack of war criminal charges). It is of course entirely possible the Japanese realized they simply could not manage the threat of more atomic weapons and the emperor decided to surrender purely to avoid more bombings. Unfortunately I don't think Hirohito ever really explained his thought process for this decision, or if he did I am unaware of it.

The plan was always the bomb and invade. The US had limited means of producing atomic bombs (about 3.5 per month), but had considered continuing using them. We don't know exactly how they would have gone about that, because they didn't plan it in advance — they were playing it by ear. They might have continued using them against cities (though they recognized that would have diminishing returns over time), they might have used them tactically (e.g. in the service of an invasion).

Only the invasion of Kyushu had been authorized by Truman so far; whether an invasion of the main Japanese home island (Honshu) would take place would depend on how that went. The Soviet invasion on Manchuria was also taking place, and it's unclear whether they might have tried to invade Hokkaido if the war had gone on (it would have been logistically difficult, but that might not have stopped Stalin).

Anyway — there is a lot of uncertainty here. It is unclear whether Japan would have held out long enough for an invasion to take place (the invasion of Kyushu would not begin until November 1). The Japanese were facing, at that point, total ruin by air, a possible US and Soviet invasion and occupation, and imminent starvation. The idea that things would last until a total invasion had taken place strikes me as somewhat unlikely, even if the war had not ended when it did. (This is also the assessment of many US military analysts at the time, for whatever that is worth.)

Hasegawa's Racing the Enemy is a good book for thinking about the ways in the US, Soviet, and Japanese high commands were thinking about the various scenarios for the end of the war. For details on US plans for future atomic bombings, see my recent article in National Geographic History.