Eikonal solvers can compute principled high frequency approximations to the propagation of waves. We describe how a fast and accurate eikonal solver—the jet marching method (JMM)—can be used for various spatial audio applications. We compute personalized interaural time differences (ITDs) for head mesh scans. These results are compared against ITDs computed using the boundary element method (BEM). The comparisons validate the use of the geometrical optics model for onset calculations. We also simulate the propagation of sound waves in rooms using the JMM, and use our computations to approximate the early part of room impulse responses. Results are promising, and future extensions are discussed.