Discover acceptance abroad is actually not as bad as it might seem at a first glance: Discover owns Diners Club International, and as a result Discover cards are accepted everywhere Diners Club cards are and vice versa.

They also have some mutual acceptance agreements with JCB and China UnionPay and others. Just because there's no explicit Discover logo on a terminal/restaurant window doesn't mean a Discover card will actually not work.

It's not quite the reach of Visa or Mastercard, but international acceptance seems to be trending up.