November is little late for visit Beijing,cause there will be chilly.I think you should go Forbidden city,lama temple,temple of heaven,Great wall?and you must go to some restauran to taste real chinese food,like hot pot etc.

Some suggestions here :)

Nature/country..

Despite the chilly weather, the temperature in Beijing Shi Hua Dong limestone park remained relatively constant throughout the 4 seasons (http://www.fshshhd.com.cn/).

This however requires a 2hr trip on bus to the countryside, from the Pin Guo Yuan train station (West Beijing).

City/suburbs..

For city experience, visit Hou Hai, a renowned pubbing location popular to the locals as well as travelers.

Summer Palace (Yi He Yuan) is also a scenic location to visit within the city perimeter. Monument enthusiasts can visit the ruined buildings of Yuan Ming Yuan (http://en.wikipedia.org/wiki/Old_Summer_Palace).

Food..

Get a taste of local fare like XinJiang lamb kebab, a specialty of the Chinese Muslim (Hui tribe) sprinkled with Fennel and salt. Also, try the renowned Quan Ju De Peking duck (www.quanjude.com.cn/direct.php).

The cool weather will also be a great time for candy hawthorn!

Other popular Beijing delights and exotic food (like scorpions..silkworms..) can be found in Wang Fu Jing Food Street (Wang Fu Jing Station)

I think the Imperial Palace and Great Wall are the places you must go!