Six days in Seoul with a child: practical questions

We are planning a six-day family break in Seoul near the end of May with two adults and a 10-year-old. I am trying to sort out the practical details: card payments versus cash, airport transport, mobile data, and whether Seoul Sky or N Seoul Tower should be booked in advance. What would you prioritize for a relaxed family itinerary, and what is late-May weather usually like?