The best option is to sell them to someone else that is going to Japan, or use them if you got any fiends that want you to buy them rice cookers.
Currency exchanges do not seem to deal in foreign coins, at least here in New Zealand (I’ve exchanged US dollars and Japanese yen, personally). The exchange rate will also differ depending on exactly what exchange you use.
If you’re trying to maximize the amount of NZD that you receive, definitely check the exchange rates offered by various currency exchanges, as other answers suggest.
If you’re trying to end up with as close to 0 JPY as possible, then denominations and coinage matter. If you exchange your money in Japan, you will be able to spend Japanese coins, but most likely only in increments of NZ $5 (or larger, if the exchange does not stock small notes). If you exchange your money in New Zealand, you will be able to buy NZ coins, but you can only spend in increments of ¥1000. So, you would want to try to spend or convert your Japanese coins before departure, and then once in New Zealand you can convert any remaining Japanese bank notes into New Zealand bank notes and coins.
Note also that the ¥500 coin is currently worth more than the smallest NZ bank note (NZ $5) – if you end up with large coinage in Japan, it might be possible to exchange that for NZD, if you find an exchange which deals in small transactions and carries the NZ $5 note. If you wanted to do everything in a single transaction, exchanging on the Japanese side would then leave a smaller maximum remainder (somewhere between ¥350 and ¥400 might be left over if you exchange in Japan, whereas in New Zealand you could be stuck with as much as ¥999 – or more, if you didn’t exchange coins for notes).
The one piece of info I don’t have is whether Japanese currency exchanges deal with small New Zealand bank notes. I know that my bank sells ¥1000 notes, but I don’t know whether Japanese exchanges would offer NZ $5 or $10 notes.
In a lot of countries it’s possible to ask your regular bank that has your bank account to procure currency for you. The exchange rate is usually pretty fair, compared to a tourist money exchange. This process often takes a day or too.
Since you worked in Japan, you probably have a local bank account. I would suggest to talk to them, tell them how much money you have left, and ask them to get you as much NZD as possible. That is convenient because as a bank they will also happily exchange your coins for local bills without a fuss.
Any leftover coins I would either put in a charity box or hand to a homeless person.
I looked at two Japanese banks that have English websites for a chat option to verify if this works, but couldn’t find one. Their FAQ also didn’t help.
The usual rule of thumb is you get a better rate at the destination, but it never hurts to check beforehand. Look online for the “sell” rate of NZ Dollars from a Japanese bank and the “buy” rate for Japanese Yen at a NZ bank. Then do the math.
If you choose Japan, the exchange service may not have small denomination NZ currency and definitely no coins, so they will exchange however much fits into the notes they have onhand and give you back the rest in Yen.
If you choose New Zealand, I would try to swap your coins and notes for the biggest denomination Yen notes you can get before leaving Japan, rather than show up with a fist full of small notes.
Any coins you have leftover should be spent at the airport or deposited into a charity box.
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