What is the best way to travel from Shanghai to Hangzhou/Suzhou?
go to Shanghai South Train Station （火车南站 - huoche nanzhan） - not to be confused with Shanghai Train Station - and buy your HZ ticket and return ticket.
It's a little more than a 1 hour trip (there are direct trains and trains with stops, so time may vary a little)
Tickets are between 50 to 90 RMB depending on the train category.
About same thing for Suzhou.
If you know your schedule ahead, just go to about any travel agent to buy your tickets, it's only a 10 RMB surcharge because they have to go to the train station for you and pick up the tickets.
Notes: go and return at Shanghai south railway station.