From what I gather in ancient Greece suicide was not widely held in high regard and was considered wrong. In some myths people sacrifice their lives for others which is considered noble but to me that is not true suicide. As how these specific deities would feel well you'd have to ask them as the brief knowledge I have is how some humans viewed suicide as wrong. As for the destination well depends on your religious views. In terms of the Underworld, and I keep referencing this because of the deities you mentioned, it could be the Asphodel Meadows. as suicide would likely not be seen nearly evil enough for Tartarus but in theory if you killed yourself because of unrequited loved your destination would be the Mourning Fields.
The individual who commits suicide remains fully conscious, trapped in the Kama Loka (the psychic or astral atmosphere surrounding and to some extent interpenetrating the physical plane), able to see and witness everything thats going on on Earth in regard to the situations and people from which they have severed themselves, and having to remain there for the destined duration of what would have been their life had they not killed themselves.
For example, if the person was destined by their Karma to have lived for 90 years in that lifetime but killed themselves at the age of 20, they will have to remain within Kama Loka for 70 years and cannot progress any further until then. They are not able to undergo the complete death process and enter into the state of Devachan or Heaven until then.
This fact of having to remain in Kama Loka for the entire remaining duration of the life they had been destined to live is not in any sense a form of punishment doled out by a Higher Power or Divine Being. It is merely due to the fact that each human being is comprised of seven parts or components (generally called the Seven Principles in the teachings of The Kybalion) and the unchangeable Laws of Nature require that these separate from one another in the right way, the right order, and at the right time, in order for everything to proceed naturally and normally at the moment of death and beyond.
The person who dies a natural death does so because their Principles have gradually and naturally run their entire course of destined duration and, of their own accord, ceased to cohere with one another. But this is obviously not the case for the person who has murdered himself or herself; the one who has taken their own life.
They find themselves just as alive afterwards, only now without the outer shell of the physical body and in even more of a trapped state than before.
What happens is really something that only the individual can decide based upon their own spiritual beliefs. It varies a lot from one religion to another.
We can't truly say what the Celts would have believed about suicide or what the Morrighan might believe as our Celtic ancestors didn't write down those beliefs. However, there is some evidence that the Celts felt that suicide was better than surrender if the battle went against them and they were in danger of being captured and held prisoner. The statue of the " Ludovisi Gaul Killing Himself and His Wife " is an indication that they might have believed that at least sometimes suicide was acceptable. https://en.wikipedia.org/wiki/Ludovisi_Gaul
Whether the Celts considered suicide unacceptable under other circumstances than defeat in battle, and therefore what their religion said about it, we have no way of knowing.
I don't believe in any myths that state people would be punished for killing themselves, What some don't understand is that when people do this, It doesn't come from a selfish or evil place. It comes from deep painful sorrow and hurt that becomes unbearable. I believe when someone commits suicide, they do the same as anyone else who passes. Punishment to those poor people would really make this a cruel existence in my opinion.