I will arrive Guangzhou Baiyun airport this Oct at 21:30 pm and what is the best and shortest way to Zhangjiajie from there .

The best and shortest way is to take a flight from Guangzhou Airport to Zhangjiajie. You'd better book this flight ticket in advance.

To Marine,
Thank you for the info. The next flight out of Guangzhou to Zhangjiajie after 21:30 is the next morning. Ok, I will take that flight in the morning. From Zhangjiajie airport, what do I take to reach the scenic areas?

Upon arrival, you could take city-bus No.4 from Zhangjiajie airport to get to downtown area and then transfer to Zhangjiajie Central Bus Station by taxi. It operates frequent buses to the scenic area.

If I am already in downtown area of Zhangjiajie, what is there to see since I am already in downtown, I might consider going around there first.
How far is downtown to the scenic areas in terms of hours? Is it convenient to just stay in downtown and go the scenic areas everyday from downtown?

Well, the coach from downtown area to the scenic spot will take 40 minutes. It is suggestd that you stay in the scenic spot so that you could have enough time at least 2 days to tour around. One entrance ticket is valid for 2-day unlimited visiting.