Bro,
That's what is recommended to most people. Suzhou, Hangzhou are not exactly what is written in the book. They are heavily commercialized touristy places. Not really my types, but I went with the flow not to disappoint my friends. I've been to further places like Zhoushan, Donji dao etc. which are not really weekend trips. If you want to go to places off the beaten path, you really don't have much choice around Shanghai (at least none that I know of). Dongji dao was probably the best of the lot with very little civilization - but very troublesome to go from Shanghai.
I believe there are some mountains with nice scenery in neighbouring Anhui province, which I haven't been to.
Huangshan, not a weekend trip (maybe 3-4 days), is another option from Shanghai. But, once again, that too is heavily commercialized
Da Ming shan, though a bit commercialized (they built a resort and a cable car from 3/4th way up the mountain to the top) is a better option. Can be done in a weekend, if you have your own transport. A bit rushed though. Its around 100 kms from Hangzhou.
Enjoy Shanghai.