I will visit shanghai next week and go to wuxi, zhejiang, zhuji for business trip,

Well, three days are enough for you to visit those cities. And you can tour around NJ and Hangzhou both. :-)
Arrange the trip in the following way:

Day 1: Shanghai-Wuxi-NJ
The high-speed train takes around an hour on the way. So after touring around, the last high-speed train schedule to NJ is at 22:36. And the duration is also an hour. After arriving, find a hotel and take the rest.

Day 2: NJ-Zhuji
Using more than half a day to tour around the city. Then take high-speed train to Zhuji in the afternoon. Then find a hotel, taste local snacks and appreciate night scene of the city.

Day 3: Zhuji-Hangzhou
Take high-speed train to get to Hangzhou in the early morning. The duration is just about half an hour. Then you will have a full day to visit the West Lake and Qinghefang Ancient Street.

Hope you like. :-)