I know very little of what to expect in Shanghai. Before I leave, here's a list of places I want to go visit or will end up visiting (all descriptions from Wikipedia):

Shanghai

• Yuyuan Gardens: located at No. 132. Anren Street in the center of the Old City next to the Chenghuangmiao area in Shanghai, China, is considered one of the most lavish and finest Chinese gardens in the region. The garden is accessible from the nearby Yuyuan Garden station on the Shanghai Metro.
• Jade Buddha Temple: is a Buddhist temple in Shanghai, China. As with many modern Chinese Buddhist temples, the current temple draws from both the Pure Land and Chan traditions of Mahayana Buddhism. It was founded in 1882 with two jade Buddha statues imported to Shanghai from Burma by sea.
• Longhua Temple: is a Buddhist Temple dedicated to the Maitreya Buddha located in Shanghai, China. Although most of the present-day buildings date from later reconstructions, the temple preserves the architectural design of a Song Dynasty monastery of the Buddhist Chan sect. It is the largest, most authentic and complete ancient temple complex in the city of Shanghai.
• Go to the top either the Pearl TV Tower or Shanghai WTC (1,612 ft)
• She Shan Hill (there's a Basilica there, an observatory and a strange earthquake monitoring device)
• Nanjing Road: is the main shopping street of Shanghai, China, and is one of the world's busiest shopping streets.
• The French Concession Quarter
• Shanghai Urban Planning Exhibition Center (huge scale model of the city)
• Xintiandi: is a car-free shopping, eating and entertainment district of Shanghai, China. It is composed of an area of restored traditional shikumen ("stone gate") houses on narrow alleys, some adjoining houses which now serve as book stores, cafes and restaurants, and shopping malls. Most of the cafes and restaurants feature both indoor and outdoor seatings. Xintiandi has an active nightlife on weekdays as well as weekends, though romantic settings are more common than loud music and dance places. Xintiandi means "New Heaven and Earth", and is considered one of the first lifestyle centers in China.
• The Bund
• The many other gardens and parks in Shanghai
• Expo 2010

Surrounding Towns/Cities (from Wikitravel)

• Suzhou is a city on the lower reaches of the Yangtze River and on the shores of Lake Taihu in the province of Jiangsu, China. The city is renowned for its beautiful stone bridges, pagodas, and meticulously designed gardens which have contributed to its status as a great tourist attraction. Since the Song Dynasty (960-1279), Suzhou has also been an important centre for China's silk industry and continues to hold that prominent position today. The city is part of the Yangtze River Delta region.
• Zhujiajiao is a very vibrant ancient water village that is the focus of this article. Formed 1,700 years ago, Zhujiajiao was an important trading hub for the surrounding countryside, and many of the buildings that can be seen there today date back to the Ming and Qing dynasties. Traditionally, goods and people were ferried on the small canals from house to house, passing under the 36 ancient stone bridges that are all still in use by locals and tourists alike.
• Nanjing means "southern capital" (versus Beijing meaning "northern capital".) It is a renowned historical and cultural city and was the capital of several dynasties over the course of Chinese history. It has many historical sites including Ming tombs that are on the UNESCO World Heritage List. It was most recently the capital of China under the Kuomintang, from 1927 until their retreat to Taiwan in 1949. With a current urban population of approximately 5 million people, Nanjing is an important center for commerce and trade in Eastern China. (note 75 minutes by high-speed rail from Shanghai!!; normally 4 hrs by "slow train")
• Ningbo is a beautiful & prosperous city in Zhejiang and also one of the most popular tourist cities in East China.
• Qibao is a small town about two square kilometers in size which is crossed by two canals. Around the canals, a large number of traditional houses, shops and restaurants are found. Recently tourism has been actively encouraged and it makes a good daytrip from Shanghai city. Although Qibao can be touristy, prices are comparatively cheap.

Further Afield (I may have difficulty getting here, especially if I don't want to fly)

• Tianmu Mountian is in Lin'an County in Northwestern Zhejiang province in eastern China. Tianmushan is located 83.2 kilometres (51.7 mi) west of Hangzhou, China. ...Tianmu mountain is best known for giant trees, waterfalls, tea, peaks surrounded by clouds, bamboo shoots, temples, and nunneries, and odd shaped rocks[3]. It is also known as a natural botanic garden because more than 2,000 species[4] of plants grow on the mountain as well as being a popular summer resort with tourists in China. Japanese Cedar trees grow to towering heights on the mountain and the west peak is noted as having the last surviving truly wild population of Ginkgo trees[5]
• Haungshan is a mountain range[1] in southern Anhui province in eastern China. The area is well known for its scenery, sunsets, peculiarly-shaped granite peaks, Huangshan Pine trees, and views of the clouds from above. Mount Huang is a frequent subject of traditional Chinese paintings and literature, as well as modern photography. Today, it is a UNESCO World Heritage Site and one of China's major tourist destinations.
• Luoyang was once one of China's Four Ancient Capitals, but the purpose of the visit here would be to see the Longmen Grottos.
• Mount Tai is a mountain of historical and cultural significance located north of the city of Tai'an, in Shandong Province, China. The tallest peak is Jade Emperor Peak (simplified Chinese: ???; traditional Chinese: ???; pinyin: Yùhuáng D?ng), which is commonly reported as 1545 metres (5069 ft) tall,  but is described by the Chinese government as 1532.7 metres (5028.5 ft). Mount Tai is one of the "Five Sacred Mountains". It is associated with sunrise, birth, and renewal, and is often regarded the foremost of the five. Mount Tai has been a place of worship for at least 3,000 years.

I think that's a pretty good list for 8 weeks of weekends...