The list of NWS measurement stations features links to the web sites of each Weather Forecast Office which all look very similar. Here is an example of the New York National Weather Service Forecast Office:
If you are looking to confirm the weather measurement for a specific date please select the “Daily Climate Report (CLI)” from the radio buttons under 1. Product>>. Then choose the proper location from the list under 2. Location>>. For most cities this would be the Airport, but for New York City only the relevant weather station is Central Park NY. Then choose the date you would like to verify in the Archived Data list under 3. Timeframe>>. Lastly click on the yellow “Go” button under 4. View>>.
Here is in example of how this works in checking data for Dec 2nd 2019.
Once you click on the “Go” button a new window will open up containing the Daily Climatological Report you requested. This report normally has information about Rainfall, Snowfall, Lowest and Highest daily temperature as well as other weather data. Here is the sample for Dec, 2nd 2019.
The relevant daily measurements are underlined in red in this screenshot for your convenience.
If you are curious about how the Snow and Rain Measurement are related to each other check this page.
Click here to find out what happens if the report shows Trace for either Rain or Daily Snow.