In US usage,
Use the elevator to floor number x?
would sound very strange. The same applies to similar sentences with stairs (stairways is not a common term in the US speech, except in technical materials).
The phrase take the elevator (or stairs) to X ... is the more common usage.
The phrase use the elevator ... would be found in circumstances not describing a specific location.
Use the elevator during business hours rather than the stairs.
In case of fire, use the stairs.
The verb used could be used to describe progress toward a specific location, but only with another verb, such as
Use the elevator to exit the building.
Use the stairs to access the roof.
Use the elevator to get to floor X