for my previous leisure visit to Korea, i used Subway Korea (by Malang) and Kakao Metro. both apps are a breeze to use, and they both state train arrival timings in real time.
Didn’t use the taxi but you need to download an app called 카카오드라이버, you’ll need to buy a SIM card to have your phone #. Then register that phone # in that app.
i just used subway and bus 100% here and walk