Beijing and Shanghai are so large that there are many nice places for staying. Anyway, it is suggested that you book a hotel located close to the main tour spots or metro station. On the other hand, you could also choose a hotel in terms of your itinerary.

AS for shopping, you could go to these wholesale markets around Beijing Zoo, or the Qipu Road in Shanghai. Cheap and trendy clothes and accessories could be found.

The acrobatics show is the best method to learn about Chinses as well the Shanghai cruise could let you enjoy the city comfortable. Both are ok in my opinion.