November Visit to South Korea

Hello, all. I'm considering the first two weeks of Nov to visit South Korea and would like to do a general or grand tour to get an overall sense of the country. Costwise I'll be traveling in the budget to mid-range. I'm not desperate to see it all and am willing to return another time to complete or "fill in" what I didn't see. I like having a general idea of where I'm going, but enjoy serendipity as a guide as much as a solid itinerary. I fly in/out of Seoul, a city I already know to my satisfaction so I won't linger there. I suppose I could rent a car but I'm told it's not necessary so I'll take busses/trains. I'll have basically 14 days boots-on-the ground. Okay, little time (even a laughable amount) for many travelers, but it's all I've got. Can any veterans out there give me some general advice, like:

--Forget the grand tour idea and concentrate.
--General direction to travel early Nov: clock or counter-clockwise, north/south direction or opposite.
--Choose another time of the year because it will be to cold.
--Pitfalls: avoid X,Y,or Z that time of the year or on a weekend, or a specific holiday date.
--Best way to visit the DMZ.
--Skip some place because it's overrated.
--Anything else you can think of that you learned that will smooth they way for me.

Many thanks in advance.

Edited by: michand1 Nov 19

Edited by: michand1