I seem to be leading a one-man crusade on travel during Chinese holidays: Spring Week (Chinese New Year's), Labor Week (May 1-8) and National Week (Oct. 1-8).
I have stayed in Shanghai all three of these holidays. The ***** five-star hotels begin to give away their rooms close to the dates, as business travel, their bread and butter, comes to a dead halt. Likewise, it is easy to upgrade on international air these weeks, as business people don't travel.
You will find the luxury rooms rates at half price or less, frequently under $100 including breakfast at an incredible buffet. The prices go down, but the luxury hotels protect their well-deserved reputations.
Yes, you will find typical Chinese tourist sites frequently overwhelmed, like walking on the Bund and Yu Yuan Gardens. But most upscale sites are like normal, like the Shanghai Museum, the City Planning Museum, etc. Right now I see an Intercontinental Hotel Pudong room at $91 including one of the best breakfast buffets in the world, putting most fancy Sunday brunches to shame. These rooms go for well over $200 most of the time.
April and May in Shanghai are nice months to visit, as is October. From June to September expect oppressive humidity and heat like New York on its worst summer days.