Seriously just pick a random city from Japan Guide or go to an onsen. Visit Kyushu, it's beautiful and nobody seems to travel there because it's too far away :P
Ideally I'd take a train out of the city and rent a car or bike in whatever smaller city I make my hub. Would love any other advice you have, and open to DMs/emails/etc. :-)
- Kurobe Gorge (industrial train ride into a beautiful deep mountain gorge)
- Kanazawa (middle size town with a beautiful garden and castle ruins - near Kurobe/Touyama)
- Izumo (100% inaka, one of the oldest shrines in Japan, traditional iron working museum, nice coast with a beautiful lighthouse, in day trip distance from the only real desert (!) in Japan in Tottori)
- Kinosaki (gorgeous onsen-only town, reachable by express train from Osaka)
- Kagoshima (has the huge active Sakurajima volcano right on the other side of the bay, many Meiji restoration landmarks, don't forgot to check what the satsuma maid group is up to)
- Hitoyoshi (a little town in a mountain valley pan in Kyushu, the mid point of the Hisatsu Line - a bit less reachable right now due to some washed out railway bridges, setting of Maitetsu VNs)
- Ikede (day trip distance from osaka, home to the Momofuku Ando Instant Ramen Museum & nice view of Osaka from the hill)
- Beppu (a not so big city that is effectively the onsen capital of the world, really - the Kannawa district that hosts the 7 hells is just bonkers)
- Enoshima (go by hanging monorail with tunnels (!!) from Ofuna, visit a beautifula island with calves, shrines, temples and botanical gardens, go back to Kamakura via Enoden - a cute old electric train that hugs back dors of peoples houses and runs on regular streets part of the way)
For other advice I would recommend that at least one of your group speaks enough Japanese to ask directions, order food, use a laundromat, shop at a supermarket, describe what you want at a barber's, tell a doctor what you're ailing, ask a staff member where the lost and found is, that kind of stuff. Also note that New Year's and Golden Week are really awkward times to go and summer is hot and humid. Make sure to talk to your GP to make sure you have whatever vaccinations you need, I'm thinking of Japanese Encephalitis (JE) in particular. Also make sure you take enough cash to get the most basic necessities if the airline manages to bungle your luggage. In short, just keep all the basic travel advice in mind and you'll be fine.
A ways through his explanation someone else came up to us to ask us where we were going, and told us that our destination was simply straight ahead, and after saying our thanks we just kept listening to the guy rattle on. That kind of thing is what I really like about travelling, being a couple of thousand miles away from home, just listening to someone go on a ramble about whatever they think is interesting to talk about.
This order also very useful if you want to buy stome stuff, as usually Tokay has the best selection but you don't want to lug it all over Japan with you - best do the shopping at the end of the trip.
This doesn't seem to be a must now that JR themselves is selling it online (though at a slightly higher price):
(Elevantion 800 above see level, 1 hour walk from Keyakidaira, which itself is 1 hour industrial train ride from Kurobe. Coincidentaly the very first onsen bath we took in Japan back in 2017. And without the cold water hose - but back then we didn't know an onsen should not be that hot. :D )