Organisms maintain themselves by harvesting free energy from their environments. While the acquisition and use of information carry unavoidable thermodynamic costs, it can also increase the amount of free energy acquired from a nonequilibrium environment. We develop a framework for analyzing this trade-off of information processing in nonequilibrium environments using stochastic thermodynamics. We derive an upper bound on the net thermodynamic gain that can be achieved by introducing any additional control mechanisms for a given system coupled to a nonequilibrium environment. We illustrate our approach with some biologically inspired examples: chemical cycles, sensing and cross-membrane transport.