I'll be traveling to Zhangjiajie early next year.

Hi, the three major communication carriers are all available there and you can easily find their service offices in ZJJ City. You should make it clear which data your mobile accepts first, GSM (China Mobile), CDMA (Telecom), or WCDMA (Unicom). Then go to a correct office to get a SIM card.

Hi Julie,

Thanks for your recommendation,
Could you advice me the prices and the packages available?

My phone accepts GSM and CDMA

Oh then, you can use China Mobile. For a reasonable charge for callings and GPRS (internet), I suggest you buy a GoTone SIM Card:
For the packages, with the monthly rent fee of CNY88, you get 200min free callings in mainland China and 300MB free data. For the extra callings, it costs CNY0.19/min. They also have CNY128 (420min, 400MB) and CNY158 (510min, 450MB) packages for your choice. You can get a SIM card for free and deposit CNY150-200 for the first time to activate the package.

Just for your reference and the exact info rests with the service office.