Was there a hell or place of suffering after death in Norse mythology?

The place of suffering was found in Helheimr, and was called Náströnd, meaning "corpse shore". This is where the impure dead, like adulterers, murderers and oath-breakers were sent. It was a cave full of snakes, with an ice-cold river of venom flowing through it. These dead were fed upon by the dragon, Nidhoggr or Nidhog, “the dastardly striking”, which would stop gnawing on the roots of Yggdrasil, to perform this feeding. https://en.wikipedia.org/wiki/Náströnd

• Helheimr was where the common people went.

Not a place of torture, unlike the Christian Hell, but more akin to the Greek Hades and other, neutral, pagan underworlds. (In Hades, for instance, the spirits of dead presumably people just wander around forlorn in the darkness. Not a great existence, but no demons poking them with pitchforks.)

There is at least one exception regarding Baldr and Nanna [See solsdottir's comment:]

Hermod rode on till he came to Hel's gate. He alighted from his horse, drew the girths tighter, remounted him, claped the spurs into him, and the horse leaped over the gate with so much force that he never touched it. Thereupon Hermod proceeded to the hall and alighted from his steed. He went in, and saw there sitting on the foremost seat his brother Balder.

...

Hermod arose, and Balder accompanied him out of the hall. He took the ring Draupner and sent it as a keepsake to Odin. Nanna sent Frigg a kerchief and other gifts, and to Fulla she sent a ring. Thereupon Hermod rode back and came to Asgard, where he reported the tidings he had seen and heard.
_{Prose Edda, Chapter 15 "The Death of Balder"}

Nanna's ability to send gifts back to Asgard implies honored status and material comfort in Hel.

It should be noted that the gloomy existence in Hel proposed by Snorri and Saxo Grammaticus were post Christian, and the Christian conception of the underworld may have influenced them. (There seems to have been a bit of a balancing act going on in terms of presenting the earlier, pagan mythology in a manner acceptable in the new era.) It's possible the common people just lived a continuation of their lives in Hel until Ragnarok.

Warriors who die in battle get to go to Asgard, either to Odin's hall Valhalla, or Freya's field Folkvangr.

Hel... is the most general name for the underworld where many of the dead dwell.

That said, there were other realms for the dead (Valhalla, Folkvang, etc.).

... apart from the fact that Hel and Hell are both realms of the dead located beneath the ground, the two concepts have nothing in common.

...where one goes after death isn’t any kind of reward for moral behavior or pious belief, or punishment for immoral behavior or impious belief.

The dead in Hel spend their time doing the same kinds of things that Viking Age men and women did: eating, drinking, fighting, sleeping, and so forth. It wasn’t a place of eternal bliss or torment as much as it was simply a continuation of life somewhere else.

Quotes from Norse Mythology for Smart People.