Are there points on Earth with less gravity?: Yes, of course, and not only on Earth, but on almost any massive body in the Universe, such as the Sun, the Milky Way, or any asteroid.
|Zero Gravity centre of mass.|
- It's a zone around its centre of mass - the centre of gravity between us.
Having said that, there are a number of conditions that need to be known.
1. It is normally inaccessible due to the high pressures and temperatures inside the massive body - for example a star, or the earth itself.
2. It is not exactly zero the gravity in the center of mass, but the global resultant of the effects of the rest of the massive bodies of the universe, which gives to each passing-point of space-time a deformation of its geometry - which is usually, due to its properties, much smaller than what would happen in the surface of the body.
3. On the other hand, any body in free fall - or orbiting around one or more other bodies, following the special theory of relativity, is subject to a minimum acceleration due to gravity, which is zero if there are no external influences on the system under examination.
Zero gravity and Low gravity on Earth
Today's satellites are capable of measuring the force of gravity at every point on Earth's surface, and with that data gravity maps like this one from NASA are made.
|Earth's surface gravity map.|
Earth's gravity draws us to the center of the planet. Actually, we notice gravity because the surface on which we lean is opposed to the movement that gravity would provoke in us towards the Earth's interior. We feel our weight because the ground prevents us from moving towards the center, because there is a resistance to that movement, while gravity "pulls" us down.