a few thoughts after 4 trips over 15 years. DH has science connections, when we are on their per diem it is a far different experience than our add-on travel days, but always worth it.
Kyoto-Nishiki market, arcade a couple blocks long of food vendors. We went with DH's Japanese hosts from Nagoya and even they had no idea what some of the food was.
Kyoto-Fushimi Inari, 100s of tori gates. It's 2-3 stops away from Kyoto on a commuter line. Jump off the train and walk a couple hundred yards. I would love to see it in the snow.
Nara-just go, it's a day trip from Kyoto. Eat hot baked potatoes from the park vendors, feed the deer.
Osaka-we did the castle, but if I were doing it again, and we got to Osaka at the end of the trip, I'd skip the high culture and look for quirky. I'd go to the Momofuku Ando Instant Ramen Museum just because. And I'd try to get tickets to the National Bunraku Theater.
Tokyo- was there only in the heat of summer, miserable. Can only imagine that winter is equally damp. I kind of doubt the river tour boats are going in the winter, but it was an interesting view of the city.
Tokyo-fish market. Was there in the 90s, have heard they have made it more tourist friendly. Work out how to get there as early as possible which means the subway might not be running, get the hotel people to help. It was a good thing to do on the day we flew out to start the jet lag transition early. I think we were up by 3:30.
Two of our best experiences were picked up from posters I saw in the subways, a Japanese circus performance, and a children's pageant/reenactment of the rise and fall of a samurai emperor at the foot of the Nagoya castle. I took photos of the posters, showed them to the concierge or our guide and insisted they help us go. We never could get baseball tickets though.
Keeping costs down-we ate a lot of meals on our own ticket in the train stations, which extend for blocks below ground. Loads of options that regular folk can afford. We grabbed Bento boxes for daytime sightseeing, soba noodles for night, even French pastry cafes. I can do most exotic Japanese food but prefer not to have fish for breakfast and DH needs his coffee. Now there are Circle Ks all over the place for more familiar snack foods and soda dependency fixes.
One weird cultural thing that may have changed-there are tons of vending machines on the streets, but it seemed you were supposed to drink your beverage AT the machine, not walk on the street with it. Once I found the Circle Ks it was easier to get a cold drink and find a bench at a park or shrine.
