Advances in data-driven signal processing have resulted in impressively accurate signal and parameter estimation algorithms in many applications. A common element in such algorithms is the replacement of hand-crafted features extracted from the signals, by data-driven representations. In this paper, we discuss low-dimensional representations obtained using spectral methods and their application to binaural sound localization. Our work builds upon recent studies on the low-dimensionality of the binaural cues manifold, which postulate that for a given acoustic environment and microphone setup, the source locations are the primary factors of variability in the measured signals. We provide a study of selected linear and non-linear spectral dimensionality reduction methods and their ability to accurately preserve neighborhoods, as defined by the source locations. The low-dimensional representations are then evaluated in a nearest-neighbor regression framework for localization using a dataset of dummy head recordings.