Tropical cyclone (TC) hazards coupled with dense urban development along the coastline have resulted in trillions in US damages over the past several decades, with an increasing trend in losses in recent years. So far, this trend has been driven by increasing coastal development. However, as the climate continues to warm, changing TC climatology may also cause large changes in coastal damages in the future. Approaches to quantifying regional TC risk typically focus on total storm damage. However, it is crucial to understand the spatial footprint of TC damage and ultimately the spatial distribution of TC risk. Here, we quantify the magnitude and spatial pattern of TC risk (in expected annual damage (EAD)) across the US from wind, storm surge, and rainfall using synthetic TCs, physics-based hazard models, and a county-level statistical damage model trained on historical TC data. We then combine end-of-century TC hazard simulations with US population growth and wealth increase scenarios (under the SSP2 4.5 emission scenario) to investigate the sensitivity of changes in TC risk across the US Atlantic and Gulf coasts. We find that not directly accounting for the effects of rainfall and storm surge results in much lower risk estimates and smaller future increases in risk. TC climatology change and socioeconomic change drive similar magnitude increases in total EAD across the US (roughly 160%), and that their combined effect (633% increase) is much higher.