One of your days should be spent across the river in the Pudong district. There are several ways to cross the river, but taking a ferry is the most fun and certainly the most scenic.
Two of the many skyscrapers you will see are particularly notable. The Oriental Pearl TV Tower was one of the first built after the Chinese government earmarked tons of money to construct Shanghai’s new urban center. As a result, it is somewhat of a symbol of this New Shanghai. It is a strange looking structure, to be sure. The pink-shaded bulbs are intended to represent pearls, but the most fun thing about the tower is that you can take an elevator to the top for a staggering view of the city. There are three levels to choose from, and the second is usually preferable to the highest. Unless it is a pristine day (rare in Shanghai), views are usually clouded at the top level.
When you are finished at the top, head to the very bottom. The wonderful Shanghai Municipal History Museum is located in the basement.
If you are game for more, the Jin Mao Tower offers a similar experience. It is the tallest building in Asia and the third tallest in the world. Again, you can take an elevator up to the top for great views.
For interesting shopping in Pudong, head to First Shanghai Yaohan, the largest department store in Asia.