Magnetic skyrmions in thin films with perpendicular magnetic anisotropy are promising candidates for magnetic memory and logic devices, making the development of ways to transport skyrmions efficiently in a desired trajectory of significant interest. Here, we investigate the transport of skyrmions by surface acoustic waves (SAWs) via several modalities using micromagnetic simulations. We show skyrmion pinning sites created by standing SAWs at anti-nodes and skyrmion Hall-like motion without pinning driven by traveling SAWs. We also show how orthogonal SAWs formed by combining a longitudinal traveling SAW and a transverse standing SAW can be used for the 2D positioning of skyrmions. Our results also suggest SAWs offer a viable approach to the transport of multiple skyrmions along a multichannel racetrack.