The large‐scale structure of Saturn's magnetosphere is determined by internal and external factors, including the rapid planetary rotation rate, significant internal hot and cold plasma sources, and varying solar wind pressure. Under certain conditions the dayside magnetospheric magnetic field changes from a dipolar to more disk‐like structure, due to global force balance being approximately maintained during the reconfiguration. However, it is still not fully understood which factors dominantly influence this behavior, and in particular how it varies with local time. We explore this in detail using a 2‐D force‐balance model of Saturn's magnetodisk to describe the magnetosphere at different local time sectors. For model inputs, we use recent observational results that suggest a significant local time asymmetry in the pressure of the hot (>3 keV) plasma population, and magnetopause location. We make calculations under different solar wind conditions, in order to investigate how these local time asymmetries influence magnetospheric structure for different system sizes. We find significant day/night asymmetries in the model magnetic field, consistent with recent empirical studies based on Cassini magnetometer observations. We also find dawn‐dusk asymmetries in equatorial current sheet thickness, with the varying hot plasma content and magnetodisk radius having comparable influence on overall structure, depending on external conditions. We also find significant variations in magnetic mapping between the ionosphere and equatorial disk, and ring current intensity, with substantial enhancements in the night and dusk sectors. These results have consequences for interpreting many magnetospheric phenomena that vary with local time, such as reconnection events and auroral observations.