Reusable water bottle
Japan has a very high standard of drinking water, most cafes or restaurants will fill up your water bottle. If you are in a country without a drinkable (to British digestion) water supply, check out my post on how to get around this. This saves me SO much money.
Reusable shopping bags
Japan is in love with single use plastic bags, but unlike many countries they are not littering the countryside. This actually creates less incentive to change! Tokyo has been arguing about introducing a ban for years. Even with the language barrier I have not had a problem asking to use my own bag.
Reusable chopsticks / cutlery
A must for me when out and about in any country. In Japan many sit down food places only give disposable wooden chopsticks. Although these are technically compostable Japan does not seem to have a composting system, with most waste being incinerated. Bring an extra napkin to wrap them in and a mini bottle of washing up liquid to ensure you can keep them clean.
The Japanese love a paper napkin individually wrapped in plastic! However even in countries without this quirk I still prefer to try and use my own napkin when I can. Paper ones are single use, and to me a waste of resources. Most will go into landfill, so will not be composted in any kind of circular system. Napkins are also useful for purchasing street food, bakery items, cleaning up spills, emergency hankies, putting in your coffee cup to mop up dregs, and lots of other uses. Bring a small bottle of laundry liquid to hand wash as needed. Roll in a towel and hang up to dry overnight. I take six for 2 people for a 2 week trip.
Great for hot drinks on the go and sake on the train!
Vegetable / bakery bags
When I am planning on doing any self catering, or taking sandwiches on a hike, I pop a couple of Bee Bee Wraps in my luggage.