Some islands that were considered part of Japan (such as Okinawa) were the sites of combat. But the invasion of the main home islands was an operation that was a ways off when the war ended owing to all the necessary preparation.

So aside from the occasional bit of sabotage, not really. One stands out in my mind: the work of Eugene Fluckey's legendary USS Barb (SS 220), a Gato-class submarine, which also holds a distinction for one of the greatest confirmed tonnages sunk by a US sub in the war.

Basically, what happened was this, embellished by various officers and crew: for her final patrol of the war, Barb had been refitted with 5-inch rockets, with the intent of doing some surface harm in part because of the paucity of Japanese targets in the water by June 1945. She hit three towns with the rockets, and devastated a fourth using the conventional deck gun, but the actual "on Japanese ground" part came later. On the evening of 22 July 1945, a party went ashore from Barb near Karafuto about 150 km from Tokyo, and laid charges on the nearby railroad tracks. This ploy worked; the retreating party got to see the train hit the section and the charges go off. (The train is represented among the chits on the Barb's battle flag.)

This, however, is not actual combat; I'm not aware of any of that happening on land. Usually, if facing actual resistance, such landings would never be considered; the actions of Barb were fairly reckless but in line with some of the more legendary commanders of the US submarine force like Fluckey and their rather competitive crews. USS Bowfin sank a dock, a crane, and a bus in the Ryukyu islands (also on her battle flag; she is moored in Pearl Harbor today), but that involved a torpedo. Subs on lifeguard patrol on the main approaches for bombing would come under fire while retrieving aircrews within easy sight of shore, but again, this is not land-based combat.

Maybe I am missing some episodes somewhere, but the answer for conventional combat is negative, though there was activity of some kind or another late in the war.

That depends if you consider Okinawa to be part of Japan at that time. NOW it's part of Japan. At that time, it was technically part of Japan but not really one of the "home islands". It was an outlier with a kind of borderline status--wholly annexed by Japan yet only sometimes part of Japan. Okinawans didn't really feel like a regular part of Japan, and many remain angry at Japan and feel they are discriminated against, and that the terrible, bloody Battle of Okinawa was so bloody because Okinawan status was so low so the imperial state didn't value Okinawan lives. I think if you asked people in 1945 if Okinawa was part of Japan, you wouldn't get a universal consensus of yes. But probably the majority would say yes. For that matter, Korea was legally part of Japan at that time, yet would people of that time consider it really part of Japan?

In any case, the Battle of Okinawa was one of the bloodiest of the war, and killed perhaps 1/4 or more of the entire civilian population of Okinawa of 300,000, and something like 14,000 US deaths. That was ground, sea and air.

Well that depends, would you consider downed air crew as "fighting" in Japan?

But for the closest large scale organized presence of ground forces you would be looking at Okinawa, which is considered part of the Home Islands.