Shanghai > Hangzhou > Nanjing > Suzhou > Shanghai seems ok. All easily doable by HS train.

If you want something off the beaten path, take a day trip to Yiwu from Hangzhou (30 min by HS Train). You can visit a 1:1 copy of the Forbidden city in Dongyang Film City (Hengdian) and go see the Yiwu International Trade Market (where you can buy tourist magnets from any destination in the world in bulk - this is where they all come from - along with other day-to-day stuff you probably use at home). HS Train from Hangzhou west to Hengdian (45 min). Then you can take the subway to the international trade market. From there take a taxi back to the train station.

Lots of good middle eastern food around the trade market.