I'm travelling to Shanghai next month and will spend a few days in town but am really interested in rural areas outside the city.

Can anyone give me any information where to stay that's not too expensive and will give me a 'locals' experience?

I'm not sure if it is advisable to stay in the "rural areas outside the city". If you take the train from Shanghai to Suzhou you will see a lot of the rural countryside and afterwards you might not be interested in it anymore. Most of the countryside is used for agriculture (water-farms for shrimp; rice paddies and delapidated buildings). I guess you could stay in some of these houses overnight for a very low price but I don't think it's safe. I would rather recommend staying in Shanghai (or Suzhou/Jiading//....) and go to the countryside by taxi or bus or bicycle.
Cheap hotels in Shanghai are Motel 168, HomeInn etc... if you search for cheap accommodation in the Q&A forum you will find some info.
Good luck!

There are plenty of "NongJiaLe" options which literally mean "Happy Farmer's Home". Many locals book these types of places in outlying areas such as Chong Ming Island. It entails staying out in the countryside in larger villas that have been set aside as guesthouses in the farming areas. Its a bit of a Chinese version of a B&B i suppose. Personal safety should not be an issue actually, though if you are one who cannot handle such a big change all at once, you MAY want to mix your trip with some city stay and some country stay just to get a good balance.