We experimentally study spatial fluctuations of the local density of states (LDOS) inside three-dimensional random photonic media. The LDOS is probed at many positions inside random photonic media by measuring emission rates of a large number of individual fluorescent nanospheres. The emission rates are observed to fluctuate spatially, and the variance of the fluctuations increases with the scattering strength. The measured variance of the emission rates agrees well with a model that takes into account the effect of the nearest scatterer only.