Ice domes and divides of the East Antarctic Ice Sheet (EAIS) are primary targets for deep ice core drilling because of their presumed stability and cold basal conditions. These characteristics are essential for preserving undisturbed and continuous stratigraphy, which is critical for interpreting climate proxies from ice core records. Here, we conduct an ensemble of transient thermomechanical simulations of the Antarctic ice sheet over the last glacial cycle to evaluate the stability of six regions identified as potential candidates for deep ice core drilling. The evolution of the basal thermal regime and its response to climate forcing are also assessed. Results indicate that domes and divides of the EAIS remained relatively stable throughout the last glacial cycle, with displacements occurring primarily within 20 to 40 km of their initial positions and elevation changes ranging from 50 to 150 m between glacial and interglacial periods. Dome migration is primarily driven by changes in local accumulation patterns and large-scale grounding-line migration. Basal temperatures and melt rates exhibit a lagged response to climate forcing of approximately 17 to 35 ka, suggesting that present-day basal thermal conditions still reflect the cooler climate of the Last Glacial Maximum. Finally, we find favourable thermodynamic conditions for the preservation of ancient ice at the base in all but one of the studied regions, and use this information to identify and map potential drilling sites across Antarctica. However, estimates of the thermal state are highly sensitive to geothermal heat flow and even minor inaccuracies in modelled ice thickness, indicating that local constraints are required to better decipher conditions at the ice-bedrock interface.