If I understand correctly, the altitude of low Earth orbit is as low as possible and yet high enough to avoid air drag for few orbits (numbers of orbits depending of the orbit's purpose, a parking orbit being quite low compare to a space station's orbit)
For planets or other celestial objects without atmosphere (e.g. Mercury, Moon), air drag is out of concerns. Thus how is the altitude for low orbit chosen?
It depends on the goals of the mission.
For photographic missions, for example, there's a tradeoff between coverage area and image resolution. The lower you are, the better the pictures, but the more pictures you need to map the entire body.
For very low orbits, note that celestial bodies aren't perfect spheres; besides the obvious concern about hitting a mountain, the irregular distribution of mass within the body perturbs the orbit; higher orbits minimize this effect.
The orbital period is often a significant factor. A low orbit around the moon takes about two hours; if you don't want to have your probe go in and out of contact every two hours, use a higher orbit.
In the particular case of the Moon, there is a disturbance that is not an atmosphere that will take you out of orbit and crash you into the body just the same. That is the irregular gravity field of the Moon. There is a tradeoff between orbital lifetime, fuel required to stay in orbit, and orbit altitude. The lower you go, the less variation you can tolerate in your orbit in order to not intersect the surface, and so the more fuel you need per month to reduce those variations to an acceptable level. From what I've seen in typical lunar orbit mission designs, that resulting effective low Lunar orbit altitude is about 50 km.
