Hi Jeremy, my wife and I are visiting her parents in Hangzhou (capital of the province next to Shanghai) on 29th April - pity our trips didn’t overlap or I’d suggest meeting up.
I would suggest getting as far out of the city as possible. Not because Shanghai isn’t a great city to explore, but because one of the most incredible things about China is the way all of the huge modern developments happen right on the doorstep of traditional rural cultures.
I would go on for ages if I had more time to type, but basically meet lots of Chinese people and eat lots of food - even if it looks funny, it usually tastes incredible. Also bear in mind that Shanghai is probably the most "western" city in China, and it’s kind of like their London. Drink some BaiJou (distilled rice spirit) - even the cheap stuff is great. Always take toilet roll out with you!
I remember the first time I went, had a huge grin on my face the whole time. Hope you have fun.
PS - Twitter and all of the other blocked sites can be accessed quite easily with a proxy, or write a basic twitter app with the twitter api and put it on your domain. It’s just the twitter domain that’s blocked there.