I recently started a thread on budget hotels in Beijing in the budget travel forum. The insights there are also applicable to Shanghai, although some of the chains are different.

But, my big Shanghai tip is to stay somewhere central, preferably near a metro station. Here is my ranking of districts:

1) Jing'an (as close to the temple as possible)
2) Xuhui (Fuxing Road is a really nice street for walking and taking pictures)
3) Luwan
4) People's Square
5) Xuijiahui (this might be part of Xuhui, but it is its own beast)
6) The Bund area
7) Gubei (a bit off the beaten path, but there are nice restaurants out there, and you get a bit more of a nature feel)

I would avoid: Zhabei, Putuo, Minhang, and anywhere on the east side of the river (Pudong).

If you do end up at a 168 or similar budget chain, buying a VIP card upon checkin (regular level for short stays, or gold card for ~5 days or more) is a complete no brainer.

The motel168.com website seems to be a bit of a disaster (e.g. they make it difficult to search for hotels that aren't in Zhabei, Putuo, or Pudong), but you could always call them, or use a third party site like ctrip (in this case, you might not get the VIP rate/benefit on your first night). Have a Shanghai map (e.g. smartshanghai.com) loaded during the booking process because you will have a miserable time if they stick you in a bad location.