The Shengsi Islands (嵊泗列岛) are in the Zhoushan Archipelago, Zhejiang, China. This is the archipelago just east of Shanghai / Hangzhou. Gouqi Dao is one of the most famous of these islands for tourism -- including fishing, gouqi harvesting, and its abandoned villages.
Gouqi Island (枸杞岛) is an island in the East China Sea, just south-east of Shanghai and east of Hangzhou. The name "Gouqi" derives from the plant which grows on it, Gouqi (Goji; Wolfberry). The island has a number of small townsites around it, and little in the way of resorts or other major tourist developments. It is primarily a fishing island, and the mussel farms draw huge revenues for China (from Japan and South Korea). The tourism industry is based around DaWang Beach (a beach on the east of the island) -- although there is not much there besides some small 4-5 story hotels and a single street of seafood restaurants. The other attraction to Gouqi are the abandoned fishing villages, which can be found around the island (with perhaps the most famous being in the north-east).
Take a ferry (slow or fast ferries available) from the pier to the south-east of Shanghai, which is called Xiaoyang. Xiaoyang pier is reachable by bus, car, taxi etc across the expansive "East Sea Bridge". You can take the Shanghai Metro to a main stop just north-east of the bridge, in Luchaogang. From here, there are buses (or taxis) going down the bridge to the pier at Xiaoyang. Buses should cost about 20-30 yuan. A taxi to the pier from Shanghai will probably cost you about 400 yuan.
Slow ferry will cost around 80 yuan (~4 hours)
Fast ferry costs 104 yuan (~2.5 hours)
Taxis: To get around the island, you will need to take taxis (most likely). There are no buses. If you bring a bike, the island is bike-able, although with steep and dangerous paved roads -- take care with the drivers who drive wayyyy too quickly on the narrow switchback roads.
Sunrise: take a trip to the North East of the Island and watch the sun rise
Dawang Beach: the main beach on the island; very underwhelming. The (life)guards will blow whistles at you and yell if you swim more than a few meters away from the beach. Worst of all, closes at 1700hrs every day. You can sneak around the fence to the east, though. Not a great place, overall.
Fishing: fishermen take groups of tourists out to fish "Old Man and the Sea" style (just a line and hook/bait and your hands), just at the mouth of the bay. It's fairly fun to fish with your hands, and you can feel when the fish bite much more easily. However, don't expect any big marlins or sharks; these are little tigerfish and guppies (which you take home to eat at the end of the hour).
Abandoned Fishing Villages: Gouqi is also famous for its picturesque abandoned fishing villages. Left mostly untouched, nature now takes back the villages as the fishermen moved into the towns and into the cities of the mainland.
Gouqi Picking: In late summer you can wander around and find "wolfberries".
Seafood: Almost every restaurant will serve seafood -- sometimes exclusively. The main food street is at DaWang Beach, running west/south west from it.
BBQ: There is also standard Chinese BBQ (串 chuàn) available just beside Dawang beach. Standard Chinese BBQ items are available (it's adequate).
Haijiao Yihao: A bar on the second floor of a cafe, just beside Dawang beach. Has a lovely terrace for sitting, drinking, and smoking. Good atmosphere, and good views of the main area of Dawang (see picture of Dawang beach, above. This bar is the open roof, beside the fake rocks, left and center of picture).
The drivers on Gouqi drive very fast and dangerously on the winding mountain roads. Take care.
There may have been drownings at Dawang Beach, as the guards there yell at you if you swim more than 5 meters away from shore, and the beach is fenced off and closed from 5pm onwards.