Can anyone suggest some free software that can visualize the charge density and/or electron localization function (ELF)? More importantly, can we determine/know those values (charge density and/or ELF) to any arbitrary position of the structure - i.e. not just the color map?
Yes, for example the Python package chemtools gives several examples of calculating the ELF from a Gaussian cube or similar wavefunction file.
At the moment, it will generate a Gaussian-compatible cube, but you can interpolate to whatever point you want. (I haven't gone through the Python code in detail, but I suspect you could get the ELF or other metric at points without generating the cube.)