Assuming your arrival is on-time around 6:20 pm (from the other thread, I'm assuming we're talking about the CA JFK-PEK flight), you won't jump through the transit/entry hoops and be able to get to town until about 8:00 pm. That means that your options for "sightseeing" are fairly limited. And many local eating places and street food will be winding down. I think you are going to be more tired than you expect, and will just want to get to a hotel room to dump your stuff and relax. But it's your call.

Due to timing and distance, I don't recommend that you try to go deeply to the center of the city such as Tiananmen area or Wangfujing. Especially do not head for the Wangfujing Night Market, which will be wrapping up by the time you could get there. For eats, a good place that continues all evening and wee hours, and is pretty lively is colloquially known as Guijie or "Ghost Street." Lots of local restaurants there at great prices, and some western offerings too. From the Dongzhimen Transport Hub (terminus for the Airport Express light rail), you'd need to head about 1 km west. Or tell a taxi driver "Dongzhimennei" and "Guijie." (characters are 东直门内 and 簋街). Or get to your hotel and have the doorman help you with the taxi. Near Guijie, there are some residential hutong areas you can walk through but at that time of evening, you won't see much activity outside especially if it is cold.

Another possibility is heading for the Sanlitun area where you'll find a variety of western, Chinese, and other Asian options, though not at bargain prices. Also plenty of drinking spots. Either taxi or Subway Line 10 to Tuanjiehu stop, Exit A and walk west away from the elevated 3rd Ring Road. This area will also be hopping at least to 11 pm-midnight. But is the face of "Modern China" not "Old China."

Having a hotel booked in either area would be helpful on logistics. And also for getting out to airport the next morning.