Wuzhen is the most popular day trip from Hangzhou — a well-preserved water town on the Grand Canal about 1.5 hours north, with stone-arched bridges over dark canals and whitewashed houses that featured in the Dream of the Red Chamber. Go on a weekday if possible; weekends bring large tour groups.
Shaoxing, 45 minutes east by high-speed rail, is the home of Chinese opera, yellow rice wine (shaoxingjiu), and the writer Lu Xun. It has a beautiful old canal district that is less touristed than Hangzhou and gives a better sense of what a Jiangnan water town looked like before preservation funds arrived.
Putuoshan, the Buddhist island mountain in the East China Sea, is accessible in about 3 hours by a combination of high-speed rail to Ningbo and ferry. One of China's four sacred Buddhist mountains, it is genuinely beautiful and strikingly peaceful for a major pilgrimage site.