The JW Marriott Hotel in Beijing has a number of good rates just above $100 for early October. This is the time of the ‘Golden Week’ in China where the whole country is seemingly on holiday.
I went to Shanghai in 2013 during Golden Week and while it was noticeably more crowded it was still very enjoyable.
The JW Marriott is universally regarded as one of the best hotels in Beijing. The average rate is more than twice as high.