Shanghai is broke into nine main districts, and 12 total, with the larger districts representing the city's outskirts. Here's what each is famous for and what to do and see in each unique area.
Huangpu District is home to Nanjing Road, and the area along the Bund. This is where most tourists start and end their tours of Shanghai. You'll find you, also, spend a lot of time in Huangpu.
Luwan District is home to some fancy stuff, including Xintiandi, a luxury shopping area. You'll also find some snazzy hotels and restaurants in Luwan, and a lot of bars. This is where the expats dwell.
Xuhai is home to the city's famous catholic cathedral, but more commonly tourists are visiting for the extensive shopping centers, markets and restaurants. This is shopper's paradise.
Changning District isn't popular with the tourists. Perhaps because it's a residential area with regular, low-income housing. You'll find locals milling around, small shops and lots of row houses.
Jing'an District is popular with the expats and is home to many expat-range housing units, which is why the city's Western restaurants are in the area. You'll also find Jing' an Temple at the heart of the district.
Putuo District is on the Western fringes of the main part of town, and houses mostly locals, residential homes and a few shops and restaurants but not much in the way for tourists.
Zhabei District is the up-and-coming chic residential area for wealthy locals and expats. There will be a spring in Western restaurants soon.
HongKou District houses a large number of the city's residents, and thus it is a great place to tour around to see the local housing situation, the local shops and cheaper, local restaurants.
Yangpu District is a cool place to walk around to see modern Shanghai in all it's natural glory, without the glitz and glamor of tourist areas.