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This study presents a methodology for determining the optimal placement of sensors along the height of buildings to minimize uncertainty in reconstructing structural response at non-instrumented floors. Recent advancements in sensing technology have expanded the application of sensor data in earthquake and structural engineering, including model validation, post-event damage assessment, and structural health monitoring. However, to lower the costs of sensor installation and maintenance-particularly at the regional scale-it is essential to strategically place sensors to maximize the value of the collected data. Because the optimal sensor configuration depends on the specific objectives of an instrumentation project, there is no universal solution to the sensor placement problem. In this study, we focus on identifying sensor locations that allow for accurate interpolation of structural responses at non-instrumented floors with minimal prediction uncertainty. This objective supports the primary goal of the California Strong Motion Instrumentation Program (CSMIP), which is to collect structural response data with the highest possible accuracy and the lowest uncertainty. The proposed method is limited to stationary excitations (e.g., ambient vibrations or distant earthquakes) and to buildings with uniform mass and stiffness distributions along their height. Under these assumptions, a Gaussian Process Regression (GPR) model is used to quantify response prediction uncertainty and minimize the total uncertainty across the building height by placing sensors at the most informative locations. The GPR model is based on a simple shear-flexural beam representation, which effectively approximates the building using very few parameters-parameters that can be estimated from limited building information. The proposed method is verified and validated using both simulated and real data. Finally, a table is proposed that can be used by strong motion networks to facilitate more quantitative decision-making regarding sensor placement. While assumptions used in this study may seem restrictive, they strike a practical balance between accuracy and simplicity for large-scale applications such as CSMIP. The extension of this work to non-stationary excitations and general building types by training the GPR model on recorded seismic data rather than random vibration theory is under development.