The answer is that inside a spherically symmetric shell of matter (your hollow earth or massive beach ball) there is no gravitational force anywhere - you will not "fall" in any direction, whether you are at the centre or not, regardless of the radius of the sphere.
This is a classic result of both Newtonian Gravity, and Einstein's General Theory of Relativity. In both cases it is called the [ ] Shell Theorem. Although, except at the centre, you are closer to one side than the other you can imagine that there is "more" farther away than there is closer, and because of the nature of the 1/r^2 law of Newtonian gravity everything cancels out. It is of course more complicated in General Relativity.
For a simple introduction, see the Wikipedia article on the Shell Theorem
You may also be interested to know that according to General Relativity time passes more slowly inside a hollow massive sphere than it does outside.
Whilst there is no gravitational force inside the sphere, and therefore no gravitational field, there is a non-zero gravitational potential - it just happens to be the same everywhere. Since the force of gravity depends on potential difference (just like voltage in the electrostatic case), if the potential is constant there can be no force. However, the potential does effect the passage of time in General Relativity, and since it is not zero inside the sphere time passes differently. Inside an "ordinary" matter sphere time passes more slowly.