I stopped at a small nursery, and asked for advice. I tried to explain that I have a "black thumb", but that doesn't translate well. I finally settled on the plant shown, and wrote down the Korean name for later research. It was also a good selling point that this plant only needs water once every 5-7 days.
Translating a Korean plant name to English is fun. As often is the case, you have to go through Latin first. The plant was called 시암 오로라. Using Naver, that turns out to be something called "Aglaonema Siam Orlala". A little more digging reveals this is commonly known as the "Chinese Evergreen", mine apparently of the Siam Orlala variety.
Best news of all was this quote from Wikipedia:
They are popular houseplants and ornamental plants for offices and shopping malls because they are among the easiest houseplants to grow. .... They tolerate a wide range of light, as well as neglect, and are relatively resistant to pests. Aglaonema flourish for years.
I'm encouraged. It might actually live for one whole month!