Single self-assembled InAs/GaAs quantum dots are a promising solid-state quantum technology, with which vacuum Rabi splitting, single-photon-level nonlinearities, and bright, pure, and indistinguishable single-photon generation having been demonstrated. For such achievements, nanofabrication is used to create structures in which the quantum dot preferentially interacts with strongly-confined optical modes. An open question is the extent to which such nanofabrication may also have an adverse influence, through the creation of traps and surface states that could induce blinking, spectral diffusion, and dephasing. Here, we use photoluminescence imaging to locate the positions of single InAs/GaAs quantum dots with respect to alignment marks with < 5 nm uncertainty, allowing us to measure their behavior before and after fabrication. We track the quantum dot emission linewidth and photon statistics as a function of distance from an etched surface, and find that the linewidth is significantly broadened (up to several GHz) for etched surfaces within a couple hundred nanometers of the quantum dot. However, we do not observe appreciable reduction of the quantum dot radiative efficiency due to blinking. We also show that atomic layer deposition can stabilize spectral diffusion of the quantum dot emission, and partially recover its linewidth.