Singapore to Pusan (S. Korea)

Hi I'm a South Korean, going to travel back from Singapore to Korea.

Our flight schedule is
Singapore -> Nanjiing (23.5 hours stay)
Nanjiing -> Yentai (1.5 hour stopover) -> Pusan

We like to take a brief tour in Nanjiing for 1 day. Are we eligible for 72 hours visa-free in Nanjiing? If not, Can we eligible for 24 hour free transit?

Thank you in advance.