We study excitation transport in a two-dimensional system of randomly assembled spins with power-law hopping in two dimensions. This model can be realized in cold atom quantum simulators with Rydberg atoms. In these experiments, due to the Rydberg blockade effect, the degree of disorder in the system is effectively tunable by varying the spin density. We study dynamics and eigenstate properties of the model as a function of disorder strength and system size and discuss potential limitations for experiments. At strong disorder we observe the absence of transport due to localized eigenstates with power-law tails. In this regime the spectral and eigenstate properties can be understood in a perturbative picture of states predominantly localized on small clusters of spins. As the disorder strength is weakened eigenstates become increasingly delocalized and appear multifractal for moderate system sizes. A detailed study of the system-size scaling of the eigenstate properties indicates that in the infinite size limit all state eventually become localized. We discuss the feasibility of observing localization effects experimentally in the spatial spreading of an initially localized excitation and identify limited system sizes and finite decoherence rates as major challenges. Our study paves the way towards an experimental observation of localization effects in Rydberg spin systems with tunable disorder.