looking for a cool neighbourhood to stay 15 days (Seoul)

Hi,
we are a couple looking for a cool neighbourhood to stay 15 days from 25th of december to the 8-9th of january.
we've found Jongno, for example, but do you have other ideas ?
we use to like walking a lot in streets in different neighbourhoods, restaurants, bars, shopping, all that Seoul people are doing and what tourists don't know about, ... parcs, ... all that is part of typical seoul way of life in general.
for example, we don't like to eat in a restaurant, sitting around other parisian people (not funny at all).
we would like to meet (not every day, of course) people who are living a pleasant life in Seoul who could show us their way to enjoy this great city.
thanks in advance for your help.
regards,
eighter/eighter