You can stay at Nanjing Lu area, from which you can reach to other part of the city conveniently including the Expo Site. From Hangzhou you can take bullet train at either Hangzhou Railway Station or Hangzhou South Railway Station.

Many thanks to Mr. Glen for your reply. May I know what time is the last train proceeding to Shanghai? If my flight reach Hangzhou at around 11pm, do I need to put a night in Hangzhou if there is no more train by that time? Then, where/which area is more convenience for me to put a night? Thanks!!

I'm afraid that there is no trains from Hangzhou to Shanghai after 11pm. You'd better stay one night in downtown Hangzhou. You may consider booking a hotel around Hangzhou Railway Station, where you could reach by shuttle bus from Hangzhou Airport and then take train to Shanghai the next day.