It is useful/appropriate to have a breastfeeding area in an airport actually, of course it's also fine to feed wherever but if your baby is distractible it's nice to have the option of a quiet place. And remember people of all cultures use airports and some women might prefer an area where no men are likely to enter. And some women travelling away from their babies will be expressing to relieve engorgement, which is hard to do discreetly in a public area.
Perhaps signs saying breastfeeding is welcome anywhere in our airport but if you would prefer privacy, the feeding rooms are here, here and here.
A general baby feeding zone would be good with a sink to wash hands, with drinking water, disposable cups and gentle lighting. Perhaps a microwave to warm bottles/food. A high chair or play pen (somewhere to put baby down for a moment while arranging bags/clothing). A clock on the wall so you can keep track of time. If flight/security announcements come through a speaker in the room, set the volume low so that they do not startle.
If you have changing facilities in the same room please make sure the bins are smell-proof, stay closed, and are regularly emptied. Preferably the changing area is separate from the breastfeeding area as a breastfeeding only area ought to be women only, really. Or potentially a lock on the door?
If the chairs have arms, padding on the arm is useful.
A counter or side table to put down a bottle of water, baby's bottle or pumping equipment helps.
Ikea have the best feeding/changing rooms I've come across.