Here are some Beijing tours which may help you to arrange your one-day trip there. https://www.travelchinaguide.com/package/beijing.htm
Beijing has many place to see and and one day is indeed insufficient.
Here are a collections of shopping places in Beijing:
https://www.travelchinaguide.com/cityguides/beijing/shopping.htm
To taste local food, I recommend Wangfujing Snack Street and Longfusi Snack market. For more, you can see:https://www.travelchinaguide.com/cityguides/beijing/dinning/snackstreet.htm

I just got back from BJ...every part of it is wonderful. Every hotel has tours running, but there is also tours outside the hotels ...much cheaper. Take one day for every place you go. Do not take two tours in one day...completely exhausting.
Must do...The Wall, Mutianyu, The Forbidden City, Summer Palace,
The Temple of Heaven.
Good advice for food...if the restaurant is full of locals, it is good. So many good places to eat. And cheap. See the markets, even if you don't buy. Very many cheap things to purchase....make sure you bargain. They are asking far too much money and will settle for a cheap price....enjoy! China is beautiful.