NOAA Weather Radio Modernization Act of 2023 or the NWR Modernization Act of 2023 This bill requires the National Oceanic and Atmospheric Administration (NOAA) to update the NOAA Weather Radio All Hazards (NWR) network. (NWR is a nationwide network of radio stations that broadcasts weather information 24-7 from the nearest National Weather Service office, including weather warnings, watches, and forecasts.) Specifically, NOAA must update NWR to expand its coverage and support its reliability, particularly in rural and underserved communities, through timely repairs, additional equipment, software upgrades, alternative means of transmissions, and other system changes. NOAA must assess and report on access to the current system to identify potential improvements.