The hotel of Beijing could be booked freely, so please take easy. As for Shanghai, it will be a little difficult to book a hotel around the Expo Park, but not a big problem in other area of this City. Well, the hotel rate during Shanghai Expo should be a little higher than other times.
It is suggested that you book a hotel at least one month in advance. I think you could ask this website for help, seems they supplies many hotels in Beijing and Shanghai. Good luck!