I have used the airport last week. Actually, it is not suggested that you take a taxi at the Airport since most of the taxi in green titled 陕B are from Xianyang City not Xi'an. In this case, you will be transfered to another cab titled 陕A to Xi'an once out of the airport expressway. If there is a green cab titled 陕A, you could hire it to Xi'an! But, I haven't found one when I arrived at the airport last week. And, there are also a kind of black cab titled 陕A, don't take it, too since this cab's cost higher~

Actually, no matter when you arrive at Xi'an Airport, you could catch the airport shuttle bus Line 1, whose terminal is the Bell Tower. From here, you could hire a taxi to the Grand New World Hotel at a flag-down price of 6RMB (7RMB after 23:00).

As Ms.Meng said above. I also suggest you to take a shuttle to the Bell Tower. Even though you find a correct taxi in airport, the driver always refuse you to pay by meter but ask for much more money. It's very safe to take a taxi in xi'an city and the fare is very cheape.