Halide perovskites are versatile semiconductors with applications including photovoltaics and light-emitting devices, having modular optoelectronic properties realizable through composition and dimensionality tuning. Layered Ruddlesden-Popper perovskites are particularly interesting due to their unique 2D character and charge carrier dynamics. However, long-range energy transport through exciton diffusion in these materials is not understood or realized. Here, local time-resolved luminescence mapping techniques are employed to visualize exciton transport in exfoliated flakes of the BA2MAn-1PbnI3n+1 perovskite family. Two distinct transport regimes are uncovered, depending on the temperature range. Above 100 K, diffusion is mediated by thermally activated hopping processes between localized states. At lower temperatures, a nonuniform energy landscape emerges in which transport is dominated by downhill energy transfer to lower-energy states, leading to long-range transport over hundreds of nanometers. Efficient, long-range, and switchable downhill transfer offers exciting possibilities for controlled directional long-range transport in these 2D materials for new applications.