I arrive in Shanghai with China Eastern on sept21. from JFK.

So you will arrive in PVG? Well, after landing and checking out, walk to the Long-distance Bus Station of the airport. There the direct buses to Suzhou are available (3h). It is fine to get a ticket on the spot. If you wish to travel by train, follow the signages to PVG metro station to take line 2 to Honqiao Railway Station within 90min, where there are high speed trains to Suzhou and it will take half an hour.