Animals must navigate changing environments to find food, shelter or mates. In mammals, grid cells in the medial entorhinal cortex construct a neural spatial map of the external environment1-5. However, how grid cell firing patterns rapidly adapt to novel or changing environmental features on a timescale relevant to behaviour remains unknown. Here, by recording over 15,000 grid cells in mice navigating virtual environments, we tracked the real-time state of the grid cell network. This allowed us to observe and predict how altering environmental features influenced grid cell firing patterns on a nearly instantaneous timescale. We found evidence that visual landmarks provide inputs to fixed points in the grid cell network. This resulted in stable grid cell firing patterns in novel and altered environments after a single exposure. Fixed visual landmark inputs also influenced the grid cell network such that altering landmarks induced distortions in grid cell firing patterns. Such distortions could be predicted by a computational model with a fixed landmark to grid cell network architecture. Finally, a medial entorhinal cortex-dependent task revealed that although grid cell firing patterns are distorted by landmark changes, behaviour can adapt via a downstream region implementing behavioural timescale synaptic plasticity6. Overall, our findings reveal how the navigational system of the brain constructs spatial maps that balance rapidity and accuracy. Fixed connections between landmarks and grid cells enable the brain to quickly generate stable spatial maps, essential for navigation in novel or changing environments. Conversely, plasticity in regions downstream from grid cells allows the spatial maps of the brain to more accurately mirror the external spatial environment. More generally, these findings raise the possibility of a broader neural principle: by allocating fixed and plastic connectivity across different networks, the brain can solve problems requiring both rapidity and representational accuracy.