Integrated water resource management (IWRM) is facing great challenges due to growing uncertainties caused by climate change (CC), rapid socio-economic and technological changes, and population growth. In the present study, we have developed different indices to assess the availability of water using an IWRM approach. These indices evaluate supply to demands, surface availability, groundwater availability, reservoirs, and environmental flow. Moreover, reliability, resilience, and vulnerability were determined. Sustainability index (SI) and sustainability index by groups (SG) were determined based on the five indices (all indices vary from 0 to 1). The impacts of climate change affect surface and groundwater availability, as do the agricultural, urban, and industrial requirements on the different supplies. We used the generalized AQUATOOL Decision Support System Shell (DSSS) to evaluate the IWRM in the Rio Grande Basin (Morelia, México). Various emission scenarios from representative concentration pathways (RCPs) were applied to the basin for the years 2015–2039 and 2075–2099. The results indicate increases in agricultural and urban demand, and decreases in surface runoff, as well as groundwater recharge. The proposed indices are useful for different approaches (decision-makers, water policy, and drought risks, among others). CC significantly affects the different proposed indices and indicates a decrease of the SI, SG1, and SG2 (i.e., less availability). For example, we found that SG2 decreased from 0.812 to 0.195 under the RCP 8.5 2075–2099 scenario, and SG2 equal to 0.252 and 0.326 for the RCP 6.0 2075–2099 and RCP 4.5 2070–2099 scenarios, respectively (values close to 0 indicate worst drought conditions).