Radio waves diffract around buildings, although light waves do not. The reason is that radio waves:

The wavelength of radio waves being much larger than light, has a size comparable to those of buildings, hence diffract from them.

Both radio and light waves are electromagnetic waves, just in different wavelength ranges. The wavelength of visible light is typically around the 400-700 nm range. Radio waves on the other hand, often wave wavelengths of a few meters long. 

For a wave to diffract around an object, the size of the object must be on the same order of the wavelength of the wave.
Hence, radio waves diffract through buildings because radio waves have much larger wavelength than light waves.