Hi Joanna,
I'm writing this foreword after I finish the writeup below and I must say... you've put me through a very emotional journey! Many good memories came back to me whilst writing this. Hmm..
Nanjing Dong Lu in Shanghai (Perpendicular to the Bund)
All roads in Shanghai are named after a place in China, so don't be too surprised to find yourself on Beijing Road for instance. The whole stretch of Nanjing Dong (East) Lu to Nanjing Xi (West) Lu is like Orchard Road, 4X the length. It is not actually advisable to walk from one end to another as you can get pretty sick of walking.
It is a vibrant part of town. You can do some shopping, but I didn't cos I find most of the same stuff in Singapore. The price diff is negligible.
You'll find little tour agencies along the street. Compare a few before committing to any. Definitely bargain. Plan at least 1 day out of Shanghai. 2 might be good. You can be done with Shanghai in 3 days, unless you are on a leisurely tour and happy to hang around 1 cafe for 1/2 a day.
Shopping in Shanghai
Quite pointless as you'll be better off buying imported goods in SG where it's cheaper. The only attraction for most will be to buy fake goods. The fake market moves around all the time so I'm quoting you the address where they are now. However, ask any Lao Wai (whiteys/foreigners) in Shanghai and they'll be able to show you the way.
fake market in PUXI (west of river, where you are staying): YanAn Lu, Nanjing Lu, Taobao Cheng (name may change)
this market will be nearer to you, but smaller. You can do last minute buys if something occurs to you on your last day.
fake market in PUDONG (east of river, where you are staying):
Science Centre train station itself. All underground, but it's huge. You can get clothes, shoes, phone covers, shawls, toys. Worth a visit even if you don't intend to buy.
xizhang Lu, Fang bang Lu, lao xi men, hua niao shi chang 老西门 花鸟市场 (bird and insects market)- very pretty animals on display for sale.
It may not be easy to find. You gain entry through a few small alleys. It's a little bit like Diagon Alley - if you read Harry Potter, you'll know what I mean. Ha
I personally find it to be the most fascinating place in Shanghai. I went back each season and nothing is ever the same.
Ju lu lu (pubbing area) - worth partying here, the Bund is a bit too "stuck up" for my taste and I usually head west for Ju Lu Lu. Go for the ones that are more popular less you run the risk of drinking backyard alcohol that are bad for you. Beer's generally safe to drink.
Xin Tian Di - is another very popular pubbing area. This is a very famous whitey (not sure if you mind this term, but all my caucasian friends in Shanghai call themselves that in good humour) hangout which is a must see. it's very near the bird and insect market (see above) so if you plan your visits to be adjacent, it might save on travelling.
lu jia bang 陆家浜路 fabric market (fake goods, tailor make stuff. they send to your hotel.)
Another favourite of mine is Tian Zi Fang at Tai Kang Lu. It's really quaint. It's a very memorable place for me. Lots of very good memories there. :D
Hangzhou
1 day to Hangzhou is definitely a good idea, once there, you can hire a local tour guide to bring you around. bargain a bit. It's not the ideal way to travel, may be some 50sgd more than if you take a taxi around, but for a non-Chinese, non-Local, you'll still see more by following them than by wasting time trying to get the cabbies to understand where you want to go. typically, the first car you get is the most comfortable, the next few vehicles they pick you up on will deteriorate, but if you expect it at the onset, you won't feel so bad.
http://en.wikipedia.org/wiki/HangzhouTrain schedule. There are 2 train stations in Shanghai. Go to the one in the South.
Nanjing
If by now, you still have some energy left, go to Nanjing. This time, go to the North railway station. it takes about 1 hour and 30 mins to reach nanjing. Don't bother with the WW2 museums and all that if you are not particularly interested in blood and gore and greviances. I took a look at the city walls for the history, and headed straight for the hotspring resorts, it was heavenly. You can dip all you want at 150RMB.
I've asked my ex-co whom i went with to send me the address. Will forward it on when it arrives.