A character with devil's sight or even just 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 (PHB 251):
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.
Compared to the Darkness spell, that does state so (PHB 230):
A creature with darkvision can't see through this darkness, and nonmagical light can't illuminate it.
The spell states that it creates blackness for which I cannot find any effects defined in game terms. There is no indication that it creates darkness or any other kind of obscured area.
However the spell states that "No light, magical or otherwise, can illuminate the area" and an area where light is absent is darkness. This is also backed up by the rules in the sense that there are 3 stages of illumination, and only darkness fits when there is no light, according to (PHB 183):
The presence or absence of light in an environment creates three categories of illumination: bright light, dim light, and darkness. Bright light lets most creatures see normally. Even gloomy days provide bright light, as do torches, lanterns, fires, and other sources of illumination within a specific radius. Dim light, also called shadows, creates a lightly obscured area. An area of dim light is usually a boundary between a source of bright light, such as a torch, and surrounding darkness. The soft light of twilight and dawn also counts as dim light. A particularly brilliant full moon might bathe the land in dim light. Darkness creates a heavily obscured area. Characters face darkness outdoors at night (even most moonlit nights), within the confines of an unlit dungeon or a subterranean vault, or in an area of magical darkness.
Therefore a character without darkvision or similar traits cannot see into the area, anyone with darkvision can only see there as if it was dim light.
Dim light in darkvison (PHB 183):
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.
Devil's sight does not have such a limitation, anyone with this trait can see normally into the Hunger of Hadar (PHB 110):
You can see normally in darkness, both magical and nonmagical, to a distance of 120 feet.
It was not really part of the question, but as others mentioned, characters inside the Hunger of Hadar are blinded and therefore cannot see anything, even if they have darkvision or devil's sight. They would need something like blindsight in order to see.