At the Grand Hyatt Shanghai, you could take the subway Line 2 and transfer to Line 1 at the People's Square. Then, please get off at Shanghai Railway Station where you could take a bullet train to arrive in Suzhou easily. Of course, you could come back at the same day. It is suggested that you purchase the return tickets in Shanghai.

For traveling in Shanghai, I think you could refer to the list here: https://www.travelchinaguide.com/attraction/shanghai/