Because the Earth's gravitational pull extends far into space most astronauts are never actually free of it. To reach a point where gravity is a millionth of that on Earth you would have to travel over 6 million kilometres away. Most spacecraft orbit the Earth within about 400 kilometres. The weightlessness that astronauts in space experience is actually due to the orbit of their space craft which achieves a state of constant free fall around the earth. And it is this state of freefall, which is occurs when an object falls towards Earth with an acceleration equal to gravity, that causes the weightlessness that astronauts experience.
Further to HarryLindhan's answer, there is a point close to us where the gravitational pull is almost nil - between the earth and moon, approximately 380,000km from Earth. An object placed here would not accelerate towards either body.