If there would be an empty room at the center of the earth, would you be weightless there? Basically yes as the mass of the earth all around you would cancel out. But it's still different than being far enough from any object of notable mass to feel the "real" weightlessness. The earth's mass would still be pulling you at every direction.
To be really weightless is technically impossible. The gravity doesn't have a maximum range. So no matter how far you'd get from any other object in space there would always be those faint tendrils of gravity from massive faraway objects pulling you closer.
The gravity at the earths near orbit, where the ISS for example is, the gravity is still quite noticeable at around 88% of that on the surface. The weightlessness you could experience there is neither the real weightlessness but the result of a free fall around the planet.
In practice however, you wouldn't need to get much further (astronomically speaking) from even the most massive celestial bodies to have their gravitational pull be close enough to zero. The moon for example is just a bit less than 300000 km away from earth. The gravitational force of earth at that distance is already only about 0,04% compared to what it is here at the surface of it.