Best city/area to stay.

In the first place, I wanna tell you that Zhejiang actually is a province and Hangzhou is its capital city. I am wondering if you refer to Zhenjiang City of Jiangsu Province. If so, it is suggested to set Nanjing as the base. High speed trains are accessible to the other two cities.

You can stay near Nanjing South Rail Station for the sake of easy access for trains. There are many hotels nearby. Chinese and western food can easily be found. But you may go a little farther for shopping, because I remember no big malls are available nearby.

I think 5 days for visiting 3 cities is a little hasty, as Gallon said, Hangzhou is the capital city of Zhejiang province, Zhejiang is not a city. Hangzhou, Shanghai, Suzhou, Wuxi, Nanjing are in a line, and there are high speed trains in those cities, it's very convenient. Shanghai is one of the biggest modern city; Hangzhou and Suzhou have same style I think, you can find ancient towns here; Nanjing is a city which is with long history, there are lots of stories for this city, it's also the capital city of Jiangsu province. if you have plan to visit Suzhou, I can give you some suggestion, haha, I live in Suzhou~Shopping mall or street is everywhere in my country~