Optimal sensor placement for fluid flows is an important and challenging problem. We propose a novel method for sensor placement that leverages recent advancements in data-driven reduced-order modeling techniques. The proposed methodology can be used in conjunction with any data-driven modeling technique that provides a linear approximation of the fluid dynamics. We use adjoint-based gradient descent to find sensor locations that minimize the trace of an approximation of the estimation error covariance matrix. We also propose an augmented objective function can is more suited for control-oriented applications. We demonstrate the performance of our method for reconstruction and prediction of the complex linearized Ginzburg-Landau equation in the globally unstable regime.