Yu Hua's To Live 余华写的«活着» remains close to my heart. I always recommend this novel to those who want to know more about China

Riding the Iron Rooster by Paul Theroux

I'll recommend all novels from Lun Xun ( 鲁迅） ， since you don't specify it the author should be Chinese or westerner.
Among all of his novels , my favourites are: New Year Sacrifice, Hometown, Kong Yiji. His tone is sharp , sarcastic, yet full of humanity.

'Death of a Red Heroine' by Qiu Xiaolong. This 2000 crime novel pits a Shanghai cop against some shady individuals who are part of the changing Chinese political system of the early 1990s.
Don't know if The Interpreter would consider the 1990s "modern China", but the book deserves a mention anyway.

Mao's Last Dancer was a great book, full of insight - it's not a novel but I'm putting it out there anyway.