There is direct shuttle bus from Suzhou to Shanghai, but the earliest bus depart around at 6:30am. Suggest you take trains to SHanghai Railway Station in early morning and then change to Airpot Bus line 5 to the airport.

Also suggest you take bullet train to Hangzhou and Suzhou. Shanghai Railway Station or South Railway Station all have many trains a day. You can you stay around South Railway Station for there are buses in the South Bus Station that can take you to the two cities if you want to go by bus.
Good Luck!

Hi, highly recommend your firstly taking a bullet train to arrive at Shanghai Railway Station, and then take the airport shuttle bus Line 5 there go to the airport.
Bullet train to Shanghai just takes about 40 minutes. You may consider D3016, D5433, D5484 and D5473. It is no need to purchase ticket in advance excepet during weekend and holiday.

Well, Shanghai has very convenient transportation system, so there are so many choice for a location. If you would like some traveling before going to Hangzhou and Suzhou, you may stay around the People's Square, Hong Kou or Jingan Temple area, Zhongshan Park. Both of the Shanghai South Bus Station (at Shanghai South Railway Station) and Shang Bus Station (at Shanghai Railway Station)has frequent buses to Suzhou and Hangzhou. So, you could look for a hotel nearby any railway station, too!