Can You Eat Fish Eyes?
Question

I need to know whether we as Muslims are allowed to eat the eyes of a fish. I was eating at a seafood restaurant with a friend and I was enjoying the head of the fish and then I ate the eye and he was quite disgusted and said that it is not allowed in Islam. Is that true?
Praise be to Allah.Is seafood halal?
Allah has permitted us all the produce of the sea . Hence we know that all parts of the fish are halal, including its skin, tail, eyes, etc.
{Lawful to you is (the pursuit of) water-game and its use for food} [al-Maidah 2:96 interpretation of the meaning]. 
The Prophet (peace and blessings of Allah be upon him) told us that it is halal (lawful) to eat dead creatures from the sea and dead fish , and no part of the fish was excluded from this permission. 
Can you eat fish eyes?
Hence we know that all parts of the fish are halal, including its skin, tail, eyes, etc.
It is strange indeed that a person could dare to forbid something that Allah has permitted. This is a very serious matter, as Allah says (interpretation of the meaning):
{O you who believe! Make not unlawful the tayyibat (all that is good) which Allah has made lawful to you, and transgress not. Verily, Allah does not like the transgressors.} [al-Maidah 5:87]
{Say: Who has forbidden the adornment with clothes given by Allah, which He has produced for His slaves, and al-Tayyibat [all kinds of halal (lawful) things] of food? Say: They are, in the life of this world, for those who believe, (and) exclusively for them (believers) on the Day of Resurrection (the disbelievers will not share them). Thus We explain the ayat (Islamic law) in detail for people who have knowledge.} [al-A’raf 7:32]
{Say: Tell me, what provision Allah has sent down to you! And you have made of it lawful and unlawful. Say: has Allah permitted you (to do so), or do you invent a lie against Allah?} [Yunus 10:59]
Allah has also warned His slave against forbidding anything without knowledge. He said (interpretation of the meaning):
{And say not concerning that which your tongues put forth falsely: This is lawful and this is forbidden, so as to invent lies against Allah. Verily, those who invent lies against Allah will never prosper.} [al-Nahl 16:116]
This person who has invented a lie against Allah by saying that it is haram to eat the eye of a fish must repent to Allah, and not go beyond the limits in talking about the Religion of Allah. He should not speak without knowledge. Even if he is put off by something or feels disgusted by it, he has no right to say that it is haram. 
Disliking certain foods does not mean prohibiting them
The Prophet (peace and blessings of Allah be upon him) hated the smell of garlic, and said: Whoever eats anything from this unpleasant plant should not approach us in the mosque. The people said, “It has become haram (forbidden), it has become haram.” When the Prophet (peace and blessings of Allah be upon him) heard what was being said, he said: O people, it is not for me to forbid something that Allah has permitted; this is just a vegetable whose smell is unpleasant. (Reported by Ahmad and Muslim, 877)
The Prophet (peace and blessings of Allah be upon him) explained that the fact that he disliked garlic and told people not to come to the mosque after eating it did not mean that it was haram.
Although the Messenger of Allah (peace and blessings of Allah be upon him) disliked the idea of eating lizard-meat, he did not forbid others to eat it, as is reported in the following story:
Khalid ibn al-Walid reported that some grilled lizard meat was brought to the Prophet (peace and blessings of Allah be upon him) and put in front of him. He stretched out his hand to take some, but one of the people present said, O Messenger of Allah, it is lizard meat, so he pulled his hand back. Khalid ibn al-Walid asked, O Messenger of Allah, is lizard haram? He said, No, but it is not known among my people and I cannot face eating it. So Khalid took some of the lizard meat and ate it, whilst the Messenger of Allah (peace and blessings of Allah be upon him) looked on. (Reported by al-Bukhari, 4981, al-Nasai, 4242, and Abu Dawud, 3300)
After explaining this answer to you, I want to warn you about something that I noticed in your question, where you said that you went to the seafood restaurant with a male friend. If this person is not your husband or a mahram (blood-relative whom you are permanently forbidden to marry), then you should fear Allah. Ask yourself: which is more serious, eating the eye of a fish or going out with a man to whom you are not related to sit and chat with him in a restaurant?
I ask Allah to protect us from all things that earn His wrath and to help us remember and fear Him. May Allah bless our Prophet Muhammad.
For more, please see these answers: 13348 , 10498 , 169813 and 70320 .
And Allah knows best.