Stupid question, but have you checked local department stores? I know they had Nintendo DSs in Home Plus in Suncheon (not sure if they have a HP in Mokpo).
Kumho World is behind the bus station. Go out the bus terminal, walk around the corner past Shinsegye Department Store and past E-Mart, and you'll see Kumho World on your right, behind the E-Mart. It's a tall building with 금호월드 written on top. It's like a smaller version of Techno Mart in Seoul, though admittedly I don't know what kind of video games they carry. Everyone's big into computer games here. Failing that, though, give E-Mart or your local department store a try.
As for places to stay, there are a bunch of motels behind the bus terminal, and thus near Kumho World. There are also blocks and blocks and blocks of love motels in Sangmu, accessible by the Sangmu subway station. There's also a Lotte Mart department store out there, should you still be looking for a Nintendo. Sangmu has tons of new love motels, so they'll be clean. More expensive than the ones behind the bus terminal, though.
There are a few motels downtown, but they're older and sometimes kind of dirty. Avoid the Pharoah, because
there are cameras in the rooms.
