It cost more than you might think at first glance. At many airports that are still growing (rather that at maximum capacity much of the time) the airport owner will often offer discounts on landing fees and, maybe other services, to new airlines as an inducement to establish routes from the airport. If an aircraft diverts to another airport the operator will usually have to pay the standard rates for landing.
Certainly in the UK the fees are paid to the airport the aircraft lands at.