Acoustofluidic devices, which combine principles of acoustics and microfluidics, have emerged as a promising platform for biological micro-object micromanipulation due to their non-invasive, accurate, rapid, and label-free qualities. Acoustofluidic devices have found utility in various biomedical applications including single-cell studies, point-of-care testing, lab-on-a-chip studies, and tissue engineering. In this work, we present novel device configurations which enable complex and high-resolution control of suspended micro-objects. The studies presented here utilize computational analysis to optimize (1) traveling surface acoustic wave device dimensions, (2) the configuration of a planar acoustic resonator that integrates a structured surface, (3) the thickness of the coupling layer and superstrate materials for bulk-wave transmission, and (4) the shape of acoustically actuated 3-D microstructures. These devices were verified experimentally to generate highly localized acoustic fields and acoustic streaming effects enabling rapid and spatially controllable particle capture, transport, and patterning. In doing so, this work demonstrates that computational analysis is an integral part of the development of acoustofluidic devices for advanced micromanipulation, which have extensive potential in biomedical applications.