General advice...not where to go or what to do...but a few little things that will make life in (or a trip to) China easier:
1. Always carry little packets of tissues. Restaurants often don't use/give napkins, or they give you a wonderful wet nap type of thing which works great for cleaning up after eating but is not so great for wiping your mouth, etc. The tissues are also very handy for the many restrooms that don't have toilet tissue and the smog-induced sniffles of winter and sweat mopping needs of summer.
2. Do not forget to get your debit/ATM card back from the machine. The machines here keep your card during the transaction and you have to hit "exit" or something to that effect at the end. When you're not used to this, it is easy to leave the card behind. Trust me...it's happened to us twice already and we don't seem to be alone in this dilemma.
3. Learn to use chopsticks (may be an obvious one!). I don't think this is the mysterious thing it once was since we all eat so much international cuisine. The rise of sushi's popularity has done a lot for westerners' chopstick skills especially. But, do a little practice if you need to beforehand. You can glance around you for ideas about how to handle different foods (I love the ritual of eating xialongbao using chopsticks and spoon). You do see a lot of western utensils in Shanghai, but really...you aren't going to eat a good Chinese meal that way. Of course, you may get stereotyped pity as we did and be brought a fork (at a Korean restaurant...no reflection on our skills as it was brought before we had food) but don't count on it. You won't be as graceful and experienced as people who have used them every day for their whole lives, but you will make it work. (Note my pitifully low hold on the chopsticks as evidence. This apparently predicts the length of one's marriage, but I will assume it does not apply to foreigners.)
5. Be cautious when walking; the traffic rules you are used to don't apply. There are zebra crossings and the little "walking man" lights at many corners in big cities, but the little green man should not be taken as an indicator you are safe to go. Be alert and watch especially for bikes, scooters and taxis. You might be acquainted with "right on red" after stopping, but here it will usually be a quick turn with no stop so beware of vehicles turning on to the street rapidly. The ideal situation is safety in numbers, aligning yourself with someone else or a group to cross. Also, motorized scooters and bikes will use the sidewalk and beep at you to get out of their way. If you want to zone out on a walk, don't take your life in to your hands on the streets; try a park.
So, those are some of my basic tips. However, much more important than bringing your tissues or following these tips, bring a sense of openness. You probably don't come to China because you want to experience everything you're used to. Yes, things are different. Different, chaotic, vibrant and amazing. And, that's only Shanghai!
I'm thinking about doing a post answering various questions I get asked/have been asked about China (including some pretty funny ones). Have a burning question? Comment or contact me and I'll do my best...