Hi~ in fact we just call it 柜台 if others know what you are talking about. But if you want to be specific, than you can say 值机柜台. Check it here, the chinese version of Wiki: Baidu http://baike.baidu.com/view/572352.htm BTW, 检票口 is another way to say 登机口 (Boarding Gate).

At the airport, check-in desk is 登记手续办理处，check-in-desk is 检票口，check-in is 登记手续办理。

Facturar el equipaje