The design of sustainable energy systems requires to enlarge the analysis beyond the traditional boundaries for including the economic, environmental, and societal needs and constraints in the decision-making process. In this regard, this work investigates the conceptual design of distributed energy systems by means of a multi-objective optimization strategy to simultaneously address the economic, environmental, and social aspects in the energy system design. Initially, the water consumption and the inherent safety indicators were introduced and evaluated through two single-objective optimization problems to enhance the analysis of the environmental and social dimensions of sustainability. Then, a framework including the total annualized cost, CO2 emissions, water consumption, grid dependence, and inherent safety index was used to perform the multi-objective analysis. To carry out a thorough and comprehensive analysis, four optimization problems including different combinations of the sustainability indicators were proposed and solved. The compromise among the objective functions was identified, and the obtained Pareto sets were explored for elucidating the changes in the design and operating conditions across the non-dominated solutions. According to results, the cost of energy can range between 0.37 and 0.63 €/kWh, the CO2 emissions can vary between 10.6 and 68.5 kgCO2/MWh, and the water consumption can be between 27.8 and 70.2 m3H2O/GWh depending on the evaluated objective. Moreover, it was determined that the safety of the energy system can be improved by increasing the use of the water electrolysis pathway to produce hydrogen and by reducing the capacity of the hydrogen storage unit.