Update: No! The guideline was updated earlier this year that from April 1, 2023 to December 31, 2024, the Korean Electronic Travel Authorization (K-ETA) is no longer required for U.S. citizens visiting Korea for 90 days or less for business or tourism.
Public transportation (both bus and subway) is great in Korea and takes you almost anywhere in the city! Transfers are also pretty easy. It's best to get a T-money card from a convenience store and charge in subway stations, etc. A helpful blog post here on T-money cards: https://blog.trazy.com/korea-subway-t-money-card-guide/ In terms of using a map, we recommend downloading the Naver Map app on your phone, rather than using Google Maps. Naver tends to give you a more accurate route. Kakao Taxi is the best app for calling taxis, but it's usually pretty easy to hail taxis on the spot too.