This paper develops a general observing strategy for missions performing all-sky surveys, where a single spacecraft maps the celestial sphere subject to realistic constraints. The strategy is flexible such that targeted observations and variable coverage requirements can be achieved. This paper focuses on missions operating in Low Earth Orbit, where the thermal and stray-light constraints due to the Sun, Earth, and Moon result in interacting and dynamic constraints. The approach is applicable to broader mission classes, such as those that operate in different orbits or that survey the Earth. First, the instrument and spacecraft configuration is optimized to enable visibility of the targeted observations throughout the year. Second, a constraint-based high-level strategy is presented for scheduling throughout the year subject to a simplified subset of the constraints. Third, a heuristic-based scheduling algorithm is developed to assign the all-sky observations over short planning horizons. The constraint-based approach guarantees solution feasibility. The approach is applied to the proposed SPHEREx mission, which includes coverage of the North and South Celestial Poles, Galactic plane, and a uniform coverage all-sky survey, and the ability to achieve science requirements demonstrated and visualized. Visualizations demonstrate the how the all-sky survey achieves its objectives.