where do I take a bus from Nanjing Road East, Shanghai to Hangzhou?

If you want to take buses, you can take a taxi to reach local Long-distance Bus Station at No. 1666, Zhongxing Road. From this bus station, you can find the direct buses for HZ.
In my opinion, the bullet trains between SH and HZ is suggested. If you want to take the bullet trains, from East Nanjing Road Station, you can take the local subway line 2 to reach Hongqiao Railway Station. There you can find the trains for HZ.