In my travels to Seoul, I have stayed at the Marriott in Banpo area (south of the river). I asked the concierge for recommendations for things you are asking, so do the same at whichever hotel you choose. As for the DMZ tour, try to go with the USO group tour. When I went, the Korean tours were full and the concierge connected me with the USO group. I think this group tour was better, although I have no basis for the comparison. From what I have been told, the Korean tour group, especially for Koreans (I am Korean by birth but a US citizen), must go through more checks before they are allowed on the tour and has more restrictions on where they are allowed to go and see.
Some of the places I would recommend are Kyungbok Palace, City Hall Plaza (where lot of people cheered during the 2002 World Cup), Soong Nye Mun (South Gate), Nam San (the peak in the middle of the city north of the Han river), etc. Check out this link for description of some of these places.
Have fun.

HJ