I live in Seoul, but from what I understand, NK's nukes aren't powerful enough to destroy the whole city with the initial blast. At best, they could take out a district (-gu). The fallout radiation would affect other districts, but people can survive if they evacuate to basements or underground garages with enough cement to protect them from gamma radiation. I imagine they would most likely target Yongsan-gu because the American army base is there, or maybe Jongno-gu, where the government is. NK is probably also likely to shell the city too in such a scenario, which would do more damage and chemical attacks would kill the most people.
However, any such attack from NK would be complete suicide for the regime. So that's why South Koreans don't worry about it too much. If the regime was about to collapse, it's more likely, but even if Kim Jong-un was mad enough to order the strike, he could also face a military coup right then and there to stop it. If tensions ever got severe enough or the regime was at imminent risk of collapsing, Seoul would probably then be evacuated too.