1. Visit an izakaya
An izakaya (居酒屋) is like a Japanese bar which also serves food to accompany the drinks. The food served is usually more substantial (and usually better) than in a normal bar.
Izakayas are places that most Japanese office workers go after work to have dinner and drinks. They are casual, usually inexpensive and very popular with office workers. It is the place to see Japanese office workers with their hair down after work - relaxing and having a few laughs over drinks after work. If you can understand Japanese and don't mind some harmless eavesdropping a little, it really offers an insight to the Japanese office culture.
An izakaya we visited at Kakunodate - the food was fantastic..
2. Stay at a ryokan hotel
Or at least go to an onsen if you are tight on budget. But if you can afford it, you have to try the experience of staying a night in a ryokan. The complete experience includes taking a bath with complete strangers in an onsen, having a kaiseiki dinner (a traditional Japanese multi-course dinner, usually with seasonal and local ingredients), another dip in the onsen after dinner, sleeping on a futon in a tatami room and having a Japanese breakfast.
Obviously not everyone likes taking a bath with strangers and sleeping on the floor.. but I think it is a really different and uniquely Japanese experience.
An onsen hotel at Zao - the hotels usually have at least 1 indoor and 1 outdoor bath
Part of a kaiseiki meal
3. Visit the food and souvenir section of a large departmental store
And buy something whilst you are there..
These are usually amazing places with a wide array of fruits, sweets, cookies, mochi, cakes and anything pretty looking and edible.
The service is usually extremely polite - if you go when the store just opens, it gets kind of pressurizing and embarrassing (for me at least).. Everyone will be bowing at you..
Japanese sweets.. usually very pretty.
Just to taste it before buying to make sure it tastes good too..
Japanese strawberries are so sweet.. I find the smaller ones
better than their more expensive and larger cousins..
4. Take the Shinkansen
It is the most efficient way to travel long distance in Japan. It is no doubt really expensive, but tourists can always buy some kind of pass (like the Japan Rail Pass or East Japan Rail pass etc) that will make long distance travel much cheaper.
The service staff on-board that goes around with a cart selling bentos, snacks and coffee is really efficient and quiet too.
(Seriously, SIA should really learn from them - not the efficiency part but the quiet part.... My experience with "Mam, CAN I GET YOU COFFEE OR TEA?" at 5am in the morning has left me kind of scared to travel with SIA...)
The Komachi express
5. Eat Sashimi
Eat raw fish of any kind.. whether it is Chirashi-don, sushi or simply just plain sashimi. Just make sure you eat at a good restaurant (and it doesn't even have to be expensive - just make sure there are lots of locals). It'd change your view of sashimi, whether you usually eat it or not.
Fresh Go-kaidon, or 5 types (of sashimi) rice