I agree that all the commercial/for-profit weather providers (weather.com, Accuweather, etc.) tend to get apocalyptic and clickbait-y with their weather predictions, but I've generally had a good experience with the National Weather Service's briefings.

I particularly like their detailed storm briefings (for this storm; it's the first "Winter Storm Monday Night into Tuesday" link under News Headlines on the New York forecast page), especially because they not only show their expected snowfall, but both a low-end and a high-end forecast so you can get a better understanding of the possible range -- e.g. for Newark their current prediction is 7.8", but the low end is 4" and the high end is 10", so you get a sense of how variable it could be.

These are more technical, but I also like to read the Forecast Discussions (found in the "Additional Forecasts and Information" section at the bottom of the New York forecast page). There's more nuance and explanation as to how the forecast was made as well as (usually) discussion of areas of uncertainty, e.g. they explicitly mention the biggest uncertainty for the city is when rain will change over to snow.