We present a fast and accurate method for predicting the thermodynamics of hydrogen solubility and trapping in alloys, which is two orders of magnitude faster than conventional ab-initio approaches. The model hinges on the finding that the solubility of H is dominated by its nearest neighbour environment. We apply the method to the problem of hydrogen redistribution in Nb-containing Zr nuclear fuel cladding, and validated it against brute-force ab-initio approaches. We find that hydrogen preferentially dissolves into the beta-Zr phase found in as-manufactured 2.5%Nb alloys, and H is likely to redistribute into the a phase following the irradiation-induced decomposition of beta-Zr. beta-Nb particles found in as-manufactured 1%Nb alloys may act as weak sinks for H, however irradiation-induced change of composition of beta-Nb particles increases their hydrogen-trapping strength. Nano-platelets formed under irradiation in these alloys are potentially even stronger hydrogen sinks, especially if induced by proton irradiation rather than neutrons.