I am visiting Beijing and Shanghai in the 2nd week of October

According to the weather forecast, it will be a little cool in Beijing then and on Oct. 11, there will be light rainfall. Cloudy days would be the majority, but the haze kinda of terrible there. If possible, bring a mask with you.

In SH city, it will be warm and the average temperature is around 72F. You will meet many cloudy days.

In the former city, you cannot miss the Forbidden City/Tiananmen Square, Temple of Heaven, Badaling Great Wall and Wangfujing pedestrian. Well, the Bird Nest and Water Cube is also worth ur time. In the latter city, the Oriental Pearl TV Tower, Jin Mao Tower, Yuyuan Garden, Nanjing Road and Zhujiajiao Ancient Town are recommended.

If you would like to see the best of the cities, to join a tour will help you a lot. I joined one through Travel China Guide. I recommended them to you there for the superb service. If you are interested, send them an email for more info at traveltravelchinaguide.com

May help!