Upvote:2
You always lose money when exchanging currency because of the bank overhead. Unless you have the old receipt (which with some companies allows you exchange back at a lower rate), then you want to limit the number of transactions.
Rather than exchanging Yen->Dollars (which for the company will be an internal Yen->Euro->Dollars), exchange Yen->Euro and deposit the money. Then in the USA, use a no-fee ATM card to withdraw your Euro as dollars. (This assumes you have a no-fee ATM card).
Alternately, find some departing Japanese tourists at the airport and offer to give them yen for the euro they no longer need.