I would like to travel to china for 7 - 10 Days in January 2017 Sole Traveller

Since you want to see the Great Wall, it is recommended to choose Beijing as your destination, for it houses the most and well-preserved Great Wall sections.
However January may not be a good time. The temperature may be 20F~30F at that time. It might be quite cold for visit. You can consider change your schedule to April, May, September, or October. Weather during these periods is moderate. And the scenes are also beautiful.