Hit me up if you nail own some solid plans, can take a day off to show you some nice mountain runs and garages with appealing stock.
Yeah you can rent just about anything here if you look around, normal places like Orix and the like will rarely have anything beyond Kei and everyday sedans, occasionally small vans and flatbeds for people needing to haul stuff (oh little tip of you want a car for the day for more or less free, find a cainz store or viva super, go in and find the cheapest biggest item you can find (6ft by 8ft plastic roofing sheet for $20 e.g.) ask to lend a flatbed to take it home; fill out some details and be on your way, unless it's a super busy one they won't
Mandate a return time for that day and you can just rock up 10 min before closing return the vehicle and get a refund on the sheet of plastic saying it's the wrong one
Don't try to do it too often or they'll ban you from lending the truck, I know because reasons.
There are some rental companies that specialize in more iconic cars though, anything from an ae86 to a vspec r34 gtr, one such place is omoshiro rent a car which does all sorts, for example:
https://www.omoren.com/en/products/detail/1
This works out about $110 - $190/day depending on how long you need it, one nice thing with omo though is there no limit to how much you drive, you could bring it back with 4K more on the clock and they wouldn't say shit as long as it comes back in one piece and with the same amount of gas
They frequently rent to foreigners too so not knowing any Japanese wouldn't be a problem if you don't,actually I've noticed several videos on YouTube of foreigners driving a panda 86 in Japan and al of them have been the same one from omo's lot lol