The development of new high-performance materials can boost the implementation of sodium-ion batteries. In this work, we report on a data-driven two-step algorithm for searching novel electrodes and solid electrolytes with superior estimated Na+ transport properties based on the crystal chemistry concept of flexibility and adaptability of polyhedral host structures to different mobile ions during the ion exchange reaction at low temperatures. At the first stage, polyanion frameworks derived from compositionally suitable NH4+-containing inorganic compounds are screened to study the dimensionality of Na+ diffusion pathways and migration barriers via the Bond Valence Energy Landscapes (BVEL) method. At the second stage, the downselected frameworks are optimized and examined using Density Functional Theory (DFT), which was adapted for the first time for the isomorphous ion exchange to model and validate the expected fast Na+ ionic diffusion. Such a screening of Inorganic Crystal Structure Database (2020) yields almost 70 compounds with anticipated high Na+ ionic conductivity to serve as potential electrodes or solid electrolytes. As a result, new promising KTiOPO4-type NaFeSO4F electrode material and langbeinite-type NaZr2(PO4)3 electrolyte that can be obtained from the corresponding NH4FeSO4F and NH4Zr2(PO4)3 parental frameworks, respectively, reveal low migration barriers in three crystallographic directions as per Nudged Elastic Band calculations.