As others have mentioned, the basic units to define the airspace are feet and nautical miles.
However, some other values are also used when navigating the airspace, and a few are from the SI system. For instance:
- pressure settings: hPa (aka millibars, mbar)
- runway lengths: meters
- visibility: meters
- temperature: centigrades
- minimum horizontal distance from obstacles: meters
To see the SI units for pressure, visibility and temperature in a real-life setting, just have a look at a TAF/METAR for any European airport.
The mixture of units can seem strange, but there is also a method to the madness. You know that whenever you hear a measurement in feet, it is about a vertical distance, and anything expressed in meters (or kilometers) will be horizontal. A small contribution to the clarity of communications.