Features:

Both elevator and spacecraft are so small compared to variations in the Earth's gravitational field that they define what are virtually ideal free-fall frames which are the elementary inertial frames. For the definition of free-fall frames and some further explication and qualifications, see Mechanics file: frame_basics.html: Free-Fall Frames .
Note it is always implied that free-fall frame without qualification means a free-fall frame NOT rotating relative to the observable universe.
As for the Earth itself, its center of mass is in free-fall in the external gravitational field of the rest of the universe to some unknown extent, and so its center of mass defines an inertial frame for the Earth which in the jargon yours truly uses is called a celestial frame. Celestial frames are also NOT rotating relative to the observable universe.
Note celestial frames have an internal gravitational field due the masses contributing to the center of mass. These can cause internal motions (i.e., motions of the masses of the celestial frame relative to the center of mass).
Only the differences in the external gravitational field relative to the mass-weighted average external gravitational field affect the internal motions. The mass-weighted average external gravitational field is often to good approximation the external gravitational field at the center of mass.
The differences are called tidal forces.
The tidal forces significantly affecting the Earth are due to the Moon and, to a somewhat smaller degree, the Sun. The main effect of these tidal forces on the Earth is to cause the tides.
Every surface point on the Earth rotates with the Earth's rotation which means every surface point is changing its direction of motion relative to the Earth's celestial frame which then means every surface point is in acceleration relative to the Earth's celestial frame.
Therefore, every surface point does NOT define exactly an inertial frame (see Mechanics file: Acceleration and Inertial Frames).
However, you can convert it to an inertial frame if you like (see Mechanics file: frame_basics.html: Non-Inertial Frames Converted to Inertial Frames; frame_basics.html: Rotating Frames and the Centrifugal Force and the Coriolis Force).
However again, the acceleration is actually so low (⪅ 0.03 m/s**2) that for most purposes (but not all purposes), you can treat every surface point as defining a LOCAL inertial frame (i.e., an inertial frame at the point and nearby surroundings) without conversion. This is why we can use Newtonian physics in the approximate inertial frame of any point on the Earth's surface for most purposes without conversion.