Some of the best traveler-focused US rewards cards, like the Chase Sapphire Reserve cards, have no foreign transaction fees, even zeroing out what Visa charges them. And these cards are okay not only with frequent travel but even foreign residential addresses (only for customers who relocate - US address required at initial signup). I have one of those, used it while living in Canada, and soon expect to use it while living in Europe.

They do of course make money by charging a high annual fee, but another commenter already explained how the rewards offered by this card can still give more in value than the annual fee costs. This is absolutely true in my case.