Edit: for some reason I'd interpreted the question as being about cycling. Leaving in case it's useful for cyclists or motorcyclists.
I've done a lot of cycling across various bits of Japan, from shorter day trips on the order of 150km to longer 1000km+ trips. One thing to keep in mind for visiting cyclists on longer road trips: this may seem obvious but Japan is very mountainous which means a lot of narrow roads with little/no shoulder, and long (sometimes multi-kilometre) tunnels. Fortunately drivers are in general, very considerate and careful around cyclists.
For shorter day trips, many large rivers/lakes in Japan have cycling/walking paths along one or both sides and make for really nice riding. In Tokyo, the Tamagawa or in Kyoto Kamogawa and Katsuragawa have paths. Lake Biwa has a really nice cycling trail as well.
One of my favourite longer routes was along the north coast of Japan between Tsuruga and the north end of Fukui. The mountain pass along no. 8 through Takefu has some nice views but a lot of climbing and tunnels. For something shorter but pretty, follow the Tamagawa from Tokyo up to Lake Okutama. As someone else mentioned, I find travelling in rural Japan a lot nicer than cycling in/near big cities.
If you have a compact one that fits in a bag, you can bring it fine on most intercity trains (though ideally you'd want to check before with the particular line). In local transit it's mostly frowned upon, especially in denser urban areas and busy lines. But you can usually always find some form of accommodation accessible by bike along the route, wherever you're going.
Folding bikes are much more common there, which helps a bit. You can go to a bike shop or a used-stuff-store ("recycle shop") and pick one up for $100-ish. Not going to be "nice" at that price, but it'll be functional.
I've done a lot of cycling across various bits of Japan, from shorter day trips on the order of 150km to longer 1000km+ trips. One thing to keep in mind for visiting cyclists on longer road trips: this may seem obvious but Japan is very mountainous which means a lot of narrow roads with little/no shoulder, and long (sometimes multi-kilometre) tunnels. Fortunately drivers are in general, very considerate and careful around cyclists.
For shorter day trips, many large rivers/lakes in Japan have cycling/walking paths along one or both sides and make for really nice riding. In Tokyo, the Tamagawa or in Kyoto Kamogawa and Katsuragawa have paths. Lake Biwa has a really nice cycling trail as well.
One of my favourite longer routes was along the north coast of Japan between Tsuruga and the north end of Fukui. The mountain pass along no. 8 through Takefu has some nice views but a lot of climbing and tunnels. For something shorter but pretty, follow the Tamagawa from Tokyo up to Lake Okutama. As someone else mentioned, I find travelling in rural Japan a lot nicer than cycling in/near big cities.