How far can a 2.4ghz router reach?

It depends on the antenna you are using. Without going into great detail about propagation, interference, and other factors to get the most range out any frequency you need a good antenna. The antenna of choice would be a directional antenna with a narrow beam-width. These using come in the form of a grid or parabolic dish. These particular types of antennas do a good job of focusing the radiated energy for the maximum distance or range. In a point to point setup with clear line of site, low interference, and clear Fresnel zone one could reach over 30+ miles.