In Tango, you can find post office's ATMs which accept credit, debit and
ATM cards, which are issued outside of Japan. English menu available. You need your card's 4-digit PIN.
VISA, VISAELECTRON, PLUS, MasterCard, Maestro, Cirrus, American
Express, Diners Club, JCB, China Unionpay and DISCOVER.
7-eleven store's ATM which offers 24/7 are not exists in Tango region so please make sure, you have enough cash with you before you leave major cities or check out post office's ATMs opening hours carefully!
Recently it is also possible to withdraw money from ATM at Lawson(convenience store). Although they are located in not easy access by public transportation in Tango. If you still interested to look at, please check out their official website in English.
https://oversea.lawson-atm.com/en/
Here is some lists of the ATMs in Tango:
MIYAZU area
Main post office in Miyazu, located in 300m from main entrance of Miyazu train station.
Address:2070-9 Tsuruga Miyazu Kyoto 626-8799 (〒626-8799 京都府宮津市鶴賀２０７０－９)
Open: 8:45-19:00(weekdays), 9:00-17:00(weekends&public holidays)
Post office located in west Miyazu, 300m from bus stop (Kisenba minatokan キセンバ港館)
Address: 1243 Shirakase Miyazu Kyoto 626-0011(〒626-0011 京都府宮津市白柏１２４３)
Open: 9:00-17:30(weekdays), 9:00-12:30(Saturday)
Post office's ATM located in shopping mall "Mipple", grand floor of the building, next to a flower shop.
Address: 3012 Hamamachi Miyazu Kyoto 626-0012 (〒626-0012 京都府宮津市浜町３０１２)
Open: 9:00-20:00(Everyday)
AMANOHASHIDATE area
Amanohashidate post office located in opposite side of Amanohashidare station.
Address:640-51 Monju Miyazu Kyoto 626-0001 (〒626-0001京都府宮津市文珠６４０－５１)
Open:9:00-17:30(weekdays), 9:00-17:00(Saturday)
When you are in Fuchu area of Amanohashidate where Kasamatsu park and Kono shrine is located, this post office is the closest for you.
Address: 433 Ejiri Miyazu Kyoto 629-2244 (〒629-2244京都府宮津市江尻４３３)
Open: 9:00-17:30(weekdays), 9:00-12:30(Saturday)
(Info updated on 29th Oct. 2016)