Should I pay in yen or dollars at the terminal?

Choose yen in most cases. Paying in yen lets your card network and issuer handle the conversion under the terms you agreed to, while choosing dollars lets the merchant or its provider set the rate, which can be less favorable. For many cards the combined cost of paying in yen is lower, but it depends on your issuer. If you want to be certain, convert the yen price at the reference rate and compare it with the dollar total offered, adding your card's own foreign transaction fee.¹