A character with darkvision that is not blinded can see into the area of the Hunger of Hadar.
According to the Sage Advice Compendium:
Magical darkness blocks darkvision only if the rules text for a particular instance of darkness says it does. For example, the darkness spell specifies that it produces a magical darkness that obstructs darkvision. That obstruction is a feature of the spell, not of magical darkness in general.
The Hunger of Hadar spell does not say that it blocks darkvision:
You open a gateway to the dark between the stars, a region infested with unknown horrors. A 20-foot-radius sphere of blackness and bitter cold appears, centered on a point within range and lasting for the duration. This void is filled with a cacophony of soft whispers and slurping noises that can be heard up to 30 feet away. No light, magical or otherwise, can illuminate the area, and creatures fully within the area are blinded.
Notably “No light, magical or otherwise, can illuminate the area”. Therefore the area is dark and a character with darkvision can only see there as if it was dim light. And characters without darkvision or similar traits cannot see there.
According to darkvison (highlight mine):
Within a specified range, a creature with darkvision can see in dim light as if it were bright light and in darkness as if it were dim light, so areas of darkness are only lightly obscured as far as that creature is concerned.