is airport directional?

They are not directional.. but you will have almost no signal directly underneath and somewhat less on top. But all sides will be pretty even.. The best position for the airport is high up in the room so it is unimpeded by furniture and other solids or self-propelled water bags.

The client then should sit at about the same plane the airport was designed to sit at.

Tell us what model and we can point out exact location of the antenna.

Not really, if you are asking about the most recent AirPort Extreme and AirPort Time Capsule models, that look like a "tower". The antennas are located right up and the top of the device and they radiate the signal in a spherical type pattern......similar to an expanding balloon.

Now, if you locate the AirPort on top of a desk, then a fair amount of signal is going to be absorbed by the desk, so the resulting general radiation pattern would be more hemispherical like than spherical.

AirPort Express.......Same thing applies except that a bit more of the signal will be absorbed by the desk or shelf that the AirPort Express rests on.

If you mounted the AirPort Express on a wall and "aimed" the Apple logo on the Express in the general direction where you wanted to focus the signal,, that might help just a bit. However, I notice no real improvement when I have tried this in the past, so it may not be worth the time and effort to try to figure out how to mount the Express on a wall, hide the wires, etc.