Shanghai is like a massive Disney Land.. it's glitzy and showy, it has heaps of cool things to look at, but it's quite impersonal, and it can be expensive for what it is. I think you can get a decent taste of Shanghai in 2-3 days (if you are excluding the Museums). Alot of walking and just simply absorbing the feeling of different neighborhoods. Must check out The Bund, Xintiandi (the pedestrian-only section), Tianzifang, East Nanjing Road (pedestrian-only stip) and People's Square.
Insider Tip:It's a pretty easy city to get around, metro is great- but be sure to get a metro card for a 20RMB deposit and then load say 30-50RMB (depending on you) as this saves you from having to line up in super long ques each time you catch the metro, just tap in/tap out system. I think of all Chinese Cities, you're least likely to encounter problems here, so no real "insider tip" needed I don't think.