I just came back from china yesterday and in my 16 days in china i have spent 5 days in beijing, the rest shuttling between chengdu, chongqing, then another 3 days in jiuzhaigou. nov should be a good time to visit because at least its after oct 1. i was there from 16 to 20 oct, and they actually sealed up the MRT lines and the forbidden city on 18 and 19 whole day IIRC. so i was v v v pissed as i was stuck in my hostel in wangfujing. for very very budget prices just stay in those hostels lo. i stayed along wangfujing which is the orchard rd of beijing.
in my opinion, 5 or 6 days max is enough for beijing even if u go slow. and what i like about beijing is the MRT lines. u can go to any of the local attractions like tian tan, gu gong, shui li fang, yi her yuan and niao chao via mrt. cabs are cheap but there are plenty of jams so MRT will be the best in my opinion!!! (im very kiam and budget)
and for great wall tours, please, for God's sake dont take those cheap 100 or 150 yuan tours as they will bring u for shopping. i went to 慕田峪 along with a good tour group and i really enjoyed myself.
all in all, beijing is fun, except the traffic, hordes of people, hordes of rude people, and bad haze.