Train from Shanghai area...advice

Our daughter has been in Nanjing studying, and we are travelling to meet her. We will be in Shanghai for 6 days, then Nanjing, Hangzhou and Suzhou. Over two weeks in total. We have been to China before, and want to take a fast train somewhere outside of Shanghai. I know that tourism dominates, but we are keen to go somewhere scenic, with some walking, and perhaps a smaller town. Any tips appreciated. We are not into group tours. I have looked at the UNESCO World Heritage sites...Thanks! Josie in Australia