Quantum networks, in which quantum information is distributed over long distances between many physical nodes, hold great promise for the realization of networked quantum computation, quantum communication, and distributed quantum sensing. A high fidelity interface between a long-lived quantum memory and optical photons for the long-distance distribution of entanglement form the fundamental building block of any practical quantum network. In recent years, integrated optomechanical crystals (OMCs) have emerged as a promising physical platform for quantum technologies, including quantum network applications. The flexible operation wavelength of OMCs, including the telecom C-band where fiber transmission losses are minimized, as well as the long lifetimes of their mechanical mode render OMCs a natural candidate for the storage and distribution of quantum information in long-distance quantum networks. However, initial demonstrations using one-dimensional nanobeam OMCs suffer from weak thermal anchoring to the substrate, resulting in low purity of the optomechanically generated single photons. To address this issue, quasi-two-dimensional (2D) OMCs have been developed, allowing for more efficient dissipation of generated thermal phonons into the cryogenic environment. In this thesis, we demonstrate the purity and coherence of optomechanically generated single photons from quasi-2D OMCs. Moreover, we directly measure the photon indistinguishability by two-photon interference through Hong-Ou-Mandel experiment....