Cities feature complex and heterogeneous topographies that create highly-variable airflow patterns and dynamics. The resulting extreme high and low winds challenge urban design's quest for maintaining a safe and comfortable environment. This study investigates these urban wind extrema by conducting large-eddy simulations (LESs) in four American cities with distinct topographic features and links the resulting winds to geometric indicators. By analyzing the profile and spatial variation of the wind extrema, the simulations illustrate that gust zones tend to occur along wind-oriented streets and on both sides of high-rise buildings, while stagnation zones are mostly located in the lee of tall or wide buildings. Potential geometric parameters explaining these winds extrema are investigated, including the plan and frontal area fraction and the sky view factor. These findings advance our ability to predict wind conditions solely based on urban geometry, and ultimately to design more resilient, sustainable, and livable cities.