In December, it might be brisk or you may be freezing your nether regions. If the weather is relatively cooperative, the Great Wall might be a good choice, but figure on half the day at least and a good portion of that getting too and from. I liked the Tian Tan (Temple of Heaven) and Jingshan park overlooking the Forbidden City. Jingshan is next to Beihai where touts will steer you into a rickshaw to see hutongs, but it's a nice walk and close in. Lama Temple, right (2-300 meters or more) off the subway stop of the same name, is a nice temple to visit if you haven't seen too many in China.
Personally, I'd avoid shopping at Silk Street where there are about 6 floors of booths with aggressive young salespeople all seemingly working for the same owner. There is an interesting (read: probable fakes everywhere) outdoor flea market (was reachable by bus or taxi only last time I went) at Panjiayuan if it is open and the weather permits. Much more interesting imo. I wouldn't say avoid Wangfujing since for example there are good bookstores, but it's full of scams, especially the "let's go to an authentic tea restaurant I know to practice my English" and the art student scam. And if it is freezing out there, you can duck into the posh Oriental Plaza shopping mall adjacent.
Sorry I couldn't help you with food, as I'm no foodie, but you are sure to stumble onto something interesting in that department. And my big day at the Summer Palace ended up being a run-through due to LONG traffic delays (before the subway expansion). Check wikitravel and That's BJ or whatever it's called these days, for more ideas of interesting places and the latter for western food.
It'd be a good idea to have at least two itineraries for changes due to weather and more perhaps for time constraints. A lot of the interesting places to go to in BJ are far from each other. The subway has greatly expanded and that helps but it still takes time to get to places. The taxis are good but too many rides will hurt your pocketbook and the traffic can be excruciatingly slow.