There is a quiet surcharge on many US cards used in Korea: the foreign transaction fee, typically around 3% of every purchase — often more than the rewards you earn back. Cards without that fee work in Korea exactly as they do at home.
Of the 100 cards in the DanHana catalog, 72 currently charge no foreign transaction fee. Grouped by issuer:
Chase (19 cards): Aeroplan® Credit Card (annual fee $195), Amazon Prime Visa (no annual fee), Chase Freedom Flex® (no annual fee), Chase Ink Business Preferred (annual fee $95), Chase Sapphire Preferred® Card (annual fee $95), Chase Sapphire Reserve (annual fee $795), IHG One Rewards Credit Card (no annual fee), IHG One Rewards Premier (annual fee $150), Ink Business Premier® Credit Card (annual fee $195), Marriott Bonvoy Bold® Credit Card (no annual fee), Marriott Bonvoy Boundless (annual fee $95), Southwest Rapid Rewards® Plus Credit Card (annual fee $99), Southwest Rapid Rewards® Premier Credit Card (annual fee $149), Southwest Rapid Rewards® Priority Credit Card (annual fee $229), United Club℠ Card (annual fee $695), United Gateway℠ Card (no annual fee), United Quest℠ Card (annual fee $350), United℠ Explorer℠ Card (annual fee $150), World of Hyatt (annual fee $95)
American Express (13 cards): American Express® Business Gold Card (annual fee $375), American Express® Gold Card (annual fee $325), American Express® Green Card (annual fee $150), Delta SkyMiles® Gold American Express Card (annual fee $150), Delta SkyMiles® Platinum American Express Card (annual fee $350), Delta SkyMiles® Reserve American Express Card (annual fee $650), Hilton Honors American Express Aspire Card (annual fee $550), Hilton Honors American Express Card (no annual fee), Hilton Honors American Express Surpass® Card (annual fee $150), Marriott Bonvoy Bevy™ American Express® Card (annual fee $250), Marriott Bonvoy Brilliant® American Express® Card (annual fee $650), The Business Platinum Card® from American Express (annual fee $895), The Platinum Card® from American Express (annual fee $895)
Capital One (8 cards): Capital One Quicksilver Cash Rewards Credit Card (no annual fee), Capital One Savor Cash Rewards Credit Card (no annual fee), Capital One SavorOne Cash Rewards Credit Card (annual fee $39), Capital One Spark Cash Plus (annual fee $150), Capital One Venture Rewards Credit Card (annual fee $95), Capital One Venture X Rewards Credit Card (annual fee $395), Capital One VentureOne Rewards Credit Card (no annual fee), REI Co-op Mastercard (no annual fee)
Citi (7 cards): AAdvantage® Platinum Select® World Elite Mastercard® (annual fee $99), Citi Strata Elite℠ Card (annual fee $595), Citi Strata Premier® Card (annual fee $95), Citi® / AAdvantage® Executive World Legend Mastercard® (annual fee $695), Costco Anywhere Visa® Card by Citi (no annual fee), Costco Business Anywhere (no annual fee), My Best Buy® Visa® Card (no annual fee)
Bank of America (4 cards): Atmos™ Rewards Ascent Visa Signature® Card (annual fee $95), Bank of America® Premium Rewards® Elite Credit Card (annual fee $550), Bank of America® Premium Rewards® credit card (annual fee $95), Bank of America® Travel Rewards credit card (no annual fee)
Discover (3 cards): Discover it® Cash Back (no annual fee), Discover it® Chrome (no annual fee), Discover it® Miles (no annual fee)
Synchrony (3 cards): Sam's Club® Mastercard® (no annual fee), Venmo Credit Card (no annual fee), Verizon Visa® Card (no annual fee)
U.S. Bank (3 cards): U.S. Bank Altitude® Connect Visa Signature® Card (no annual fee), U.S. Bank Altitude® Go Visa Signature® Card (no annual fee), U.S. Bank Altitude® Reserve Visa Infinite® Card (annual fee $400)
Wells Fargo (3 cards): Wells Fargo Autograph Journey℠ Card (annual fee $95), Wells Fargo Autograph® Card (no annual fee), Wells Fargo Choice Privileges® Select Mastercard® (annual fee $95)
Bilt (2 cards): Bilt Blue Card (no annual fee), Bilt Palladium Card (annual fee $495)
Acorns (1 cards): Acorns Debit Card (Mighty Oak) (no annual fee)
Apple (1 cards): Apple Card (no annual fee)
Barclays (1 cards): JetBlue Plus Card (annual fee $99)
Fidelity (1 cards): Fidelity® Rewards Visa Signature® Card (no annual fee)
Nordstrom (1 cards): Nordstrom Credit Card (no annual fee)
Robinhood (1 cards): Robinhood Gold Card (no annual fee)
SoFi (1 cards): SoFi Unlimited 2% Credit Card (no annual fee)
One tip at the register: if a Korean merchant offers to charge you in dollars, choose Korean won (KRW) instead. Dollar checkout is DCC (dynamic currency conversion) using the merchant's rate, which is usually worse; paying in won lets the card network's exchange rate apply.
If you travel often or spend long stretches in Korea, keeping one no-foreign-fee card in your wallet is the simple fix. Not sure which of your cards qualifies? The overseas-purchase mode in the DanHana recommender compares your own cards for exactly this.