Raster image correlation spectroscopy (RICS) is a powerful method for measuring molecular diffusion in live cells directly from images acquired on a laser scanning microscope. However, RICS only provides single average diffusion coefficients from regions with a lateral size on the order of few micrometers, which means that its spatial resolution is mainly limited to the cellular level. Here we introduce the local RICS (L-RICS), an easy-to-use tool that generates high resolution maps of diffusion coefficients from images acquired on a laser scanning microscope. As an application we show diffusion maps of a green fluorescent protein (GFP) within the nucleus and within the nucleolus of live cells at an effective spatial resolution of 500 nm. We find not only that diffusion in the nucleolus is slowed down compared to diffusion in the nucleoplasm, but also that diffusion in the nucleolus is highly heterogeneous.