Getting to Zhangjiajie from Changsha Airport

Hello All,

We are trying to get to Zhangjiajie from the airport and we are wondering how much it might cost to hire a private driver and car to take our family of 4. From Google Maps it looks like a 4.5 hour journey. We know there are trains but the timeline for us would be tight to catch one on our travel day. Any advise on how to book a driver and estimated cost for this option would be greatly appreciated. Thank you so much!