The well-established Consistent Adjoint Driven Importance Sampling (CADIS) and the Forward Weighted Consistent Adjoint Driven Importance Sampling (FW-CADIS) hybrid Monte Carlo/deterministic techniques have dramatically increased the efficiency of neutronics simulations, yielding accurate solutions for increasingly complex problems through full-scale, high-fidelity simulations. However, for full-scale simulations of very large and geometrically complex nuclear energy systems, even the CADIS and FW-CADIS techniques can reach the CPU and memory limits of all but the very powerful supercomputers. In this work, three mesh adaptivity algorithms were developed to reduce the computational resource requirements of CADIS and FW-CADIS without sacrificing their efficiency improvements. First, a macromaterial approach was developed to enhance the fidelity of the deterministic models without changing the mesh. Second, a deterministic mesh refinement algorithm was developed to generate meshes that capture as much geometric detail as possible without exceeding a specified maximum number of mesh elements. Finally, a weight window (WW) coarsening (WWC) algorithm was developed to decouple the WW mesh and energy bins from the mesh and energy group structure of the deterministic calculations. By removing the memory constraint of the WW map from the resolution of the mesh and the energy group structure of the deterministic calculations, the WWC algorithm allows higher-fidelity deterministic calculations that, consequently, increase the efficiency and reliability of the CADIS and the FW-CADIS simulations. The three algorithms were used to enhance an FW-CADIS calculation of the prompt dose rate throughout the ITER experimental facility. Using these algorithms increased both the number of mesh tally elements in which nonzero results were obtained (+23.3%) and the overall efficiency of the calculation (a factor of >3.4). The three algorithms enabled this difficult calculation to be accurately solved using an FW-CADIS simulation on a 94-CPU computer cluster, eliminating the need for a world-class supercomputer.