Located in the East China Sea (just off of the larger island of Zhoushan) is one of the four sacred mountains of Buddhism, Putuo Shan. Although a mere 297 meters (974 feet) above sea level, Putuo Shan's landscape is one of rocky escarpments, some nice, sandy beaches, and a collection of monasteries that line the low-lying ridges and valleys of this valuable pilgrimage site. Small enough to walk across within a few hours, Putuo Shan is still at least a full day's trip if you want a true sense of its mystique.
You may ascend the mountain to see the various pagodas and other religious sites or take the cable car to Huiji Monastery at the top. Shuttle buses also provide transportation between the temples, which can be useful if you aren't looking to foot it all day. Then again, if you just want to relax, the two beaches on the island (Hundred Step Beach and Thousand Step Beach) have basic facilities and entertainment. A great day trip for the escapist or the cultural wayfarer, put Putuo Shan on your itinerary if you're looking for a day or two out of Shanghai.
Note:There a number of options of bus/car and ferry between the island and Shanghai, the fastest of which will take you about 2 hours in total. Then again, if you're looking for cheap, the slow ferry could take up to 12 hours!