Diminishing supplies and population growth are stressing the limited water resources in many areas. A significant - but underutilized - water resource is reclaimed water, i.e., treated wastewater that is reintroduced for various purposes. In this paper, we present a cost-effective reclaimed water network design for irrigating public and agricultural areas using two-stage stochastic binary programming with random recourse. We consider both construction and energy costs expanded during a twenty-year period. By introducing binary variables that indicate discrete pipe and pump sizes, the nonlinear hydraulic equations, such as the Hazen-Williams equation, are linearized in system formulation. We consider uncertain reclaimed water demands, temporal and spatial population changes with two-stage construction decisions. In order for the system to meet significantly higher demands during the peak times, we consider two pumping conditions: one with average demands, which is used to compute the average energy consumption, and the other with peak demands, which is used for pipe size and pump station capacity selection. We apply our methodology to design a reclaimed water network for a realistic municipal system under estimated demand and population scenarios. We present the optimal total cost and system design, and examine the sensitivity of the system to model parameters.