Take a 10-Day Trip to China for the Price of an Air Ticket
Groupon currently offers a 10-day trip to Beijing and Shanghai for $ 750-1020 (including a $ 100 tax) from sixteen major US cities, not much more than the cost of a round-trip plane ticket. The deal includes hotel accommodation and about half of your breakfast and lunch. It also includes some guided tours, for better or worse. There is a $ 380 commission for traveling alone, so this is best for couples.
You cannot extend your stay, you will fly to Beijing and depart from Shanghai, so travel options are limited. It looks like you could stay in Shanghai while everyone is leaving for some nearby cities if you book your own hotel.