I heartily recommend getting someone to drive you out about 1 hour west outside Shanghai, to an ancient town named Zhujiajiao, for a view of old China. 'Old China' is apparently rare enough that a lot of Chinese visit there! Shanghai, while different from what we are normally accustomed to, is a huge high rise city with an Asian favor, yet parts of it I had to remind myself I was not strolling about Vienna! A colleague of mine and I arranged thru our hotel to have a private car and driver for a half day, so we could get to Zhujiajiao.
Largely the city is somewhat expansive and not with the crowded spaces characterizing many European ancient towns. While I greatly enjoyed taking a 24mm shift lens as my ONLY lens on a trip to Europe, I never really felt the need in Shanghai. I have gone into one very tall high rise (Shanghai World Financial Center with highest observation level floor in the world), and would not have found a shift lens valuable at all...too high up!
Don't bother taking a taxi to/from the airport and downtown. Much nicer and faster and less expensive to take the Maglev train.