How can I unblock airports without paying?
You have to work to get to specific levels on the previous airport. Then you can unlock them
As it said in the previous reply, you simply need to reach a certain level (that means a lot of XPs) of the previous to unlock the next one.
In addition to this, if you would like to unlock the next one ASAP, I suggest you to opt for a small trick that do short haul flights very frequently due to you gain same XPs on a certain aircraft type, no matter what (while you have take distance in consideration for sliver plane mining). I remember sometimes smaller planes in a certain category earns more XPs, such as A333 earns more XPs but less sliver planes than B77W if my memory was right.