Question

Does the milky way revolve around anything

Answer 1

The milky way is a Galaxy an it has its own rotating objects and they produce rotational motion. Which makes the Galaxy almost stable.
Actually motion is not a applicable for single object it is always with respect to something else with uniform or non uniform velocity.
Motion is measured as the change in place or size of the object with respect to one frame of reference. so we can't say fundamentally if our milky way galaxy it's stable or not we need something which we can relate to the frame of reference.