Seoul

A palace at opening, then a night market. The days stay in one city, not a rush across it.

Good to know

Go: Do the palace in the morning and the market at night. Midday is for a cafe and the subway.
Skip: Skip a second palace on the same day. The lanes between them are the better hour.
Eat: Barbecue or a noodle shop in Ikseon-dong. Share one grill if you are two people.
Entry: South Korea has a visa waiver for many passports and K-ETA or a visa for others. Check which one applies to you.
Timing: July and August are humid, with heavy rain. May, October are easier.

Gyeongbokgung at opening
$3
Bukchon · morning
The changing of the guard is short. The halls are the visit.
Bukchon lanes
Free
Bukchon · morning
The hanok streets ask you to keep quiet. Walk through, do not stop in a doorway.
A grill for two
$30
Ikseon · evening
One portion of meat and the banchan. A second meat order is the splurge.
Gwangjang market
$12
Ikseon · evening
Bindae-tteok or mayak gimbap from a stall with a queue.
Hongdae at night
$18
Hongdae · evening
Street performers are free. The clubs have a cover.
Hangang park
Free
Jamsu · afternoon
Rent a mat, not a cruise. The park is the plan.
Namsan, if the air is clear
$10
Bukchon · afternoon
Go only on a clear day. The cable car is optional.
A neighborhood cafe
$8
Ikseon · afternoon
One coffee. The photo stops are every third door.

A typical cost in US dollars, so you can decide before you open a booking site. Not a live fare.