Firstly:
Visiting graves is a prescribed Sunnah for men, if it is done for the purpose of taking them as a reminder and a lesson, and offering supplication for the Muslim dead, because of the report narrated by Muslim (977) from Buraydah ibn al-Husayb (may Allah be pleased with him), who said: The Messenger of Allah (blessings and peace of Allah be upon him) said: “I used to forbid you to visit graves, but now visit them, for they are a reminder of the hereafter.”
An-Nawawi (may Allah have mercy on him) said:
The scholars are unanimously agreed that visiting graves is Sunnah for men. End quote.
Shaykh al-Fawzan (may Allah preserve him) said:
Visiting graves is prescribed for men, but not for women, for the purpose of offering supplication for the dead, asking for forgiveness for them and praying for mercy for them if they were Muslims, and for the purpose of seeking a reminder, reflecting and softening hearts by seeing the graves and being reminded of the various states in which the dead will be in their graves.
End quote from Al-Muntaqa min Fatawa al-Fawzan, 41/15.
Ibn `Uthaymin (may Allah have mercy on him) said:
If a person visits graves, let him do that for the purpose of seeking a reminder and not for emotional reasons. Some people visit the graves of their fathers or mothers for emotional reasons, out of compassion and love. Although this is human nature, it is best to visit graves for the reason mentioned by the Prophet (blessings and peace of Allah be upon him), which is to be reminded of the hereafter and of death, for those who are in their graves now were like you yesterday, walking on the surface of the earth, and now they lie beneath the ground and their situation is connected to their deeds; they have no power to add one good deed to their credit or to remove one evil deed from their record. So let this be a reminder.
End quote from Durus wa Fatawa al-Haram al-Madani, p. 51.
In order for it to be permissible to visit graves, it is stipulated that one should not travel specifically for that purpose, because the Prophet (blessings and peace of Allah be upon him) said: “No one should travel for the purpose of visiting (any mosque) except three: Al-Masjid Al-Haram (in Makkah), this mosque of mine (in Madinah) and Al-Masjid Al-Aqsa (in Al-Quds/Jerusalem).” (Narrated by Al-Bukhari and Muslim).
The scholars of the Permanent Committee said:
It is prescribed for men, but not women, to visit graves if they are in the same city – that is, without travelling for that purpose – in order to reflect and offer supplication for them if they were Muslims, because the Prophet (blessings and peace of Allah be upon him) said: “I used to forbid you to visit graves, but now visit them, for they will remind you of the hereafter.”
End quote from Fatawa al-Lajnah ad-Da’imah, 1/434.
Shaykh Ibn `Uthaymin (may Allah have mercy on him) said: It is not permissible for anyone to travel expressly for the purpose of visiting some grave, no matter who the occupant of this grave is.
End quote from Fatwa Nur `ala ad-Darb, 7/196.
Secondly:
Honouring parents continues after they die, and that is done by offering supplication for them, upholding ties with their relatives, carrying out their last requests as written in their wills, honouring their friends, giving charity on their behalf, doing Hajj and `umrah on their behalf if they did not do Hajj and `umrah, paying off their debts, and carrying out any duties that they owed towards their friends.
The scholars of the Permanent Committee for Ifta’ said:
The Sunnah indicates that it is prescribed to honour parents after they die, by offering supplication for them, carrying out their last requests as written in their wills, upholding the ties of kinship which one only has through them, and honouring their friends.
End quote from Fatawa al-Lajnah ad-Da’imah, 25/182.
Shaykh Ibn Baz (may Allah have mercy on him) said:
Part of honouring one’s parents is giving charity on their behalf, offering supplication for them, and doing Hajj and `umrah on their behalf.
End quote from Majmu` Fatawa Ibn Baz, 8/344.
And he (may Allah have mercy on him) said:
There are five things: praying for them, which refers to supplication; that also includes the funeral prayer.
Praying for them also means praying for mercy for them, which is the most important duty and one of the greatest acts of kindness towards them in life and in death.
That also includes praying for forgiveness for them, and asking Allah to forgive them for their bad deeds. This is another of the greatest acts of kindness towards them during their lifetime and after they die.
Fulfilling their promises after they are gone, and carrying out their last requests as written in their will. What is required of the child, male or female – is to carry out those requests if they are in accordance with Islamic teachings.
The fourth matter is honouring their friends. If your father and mother had friends, loved ones and relatives, then you should treat them kindly and appreciate the fact that they were your parents’ friends and not forget that. This is done by speaking kind words and being generous towards them if they are in need of help, and doing all kinds of kind deeds that you are able to do. This is honouring your parents after they die.
The fifth matter is upholding the ties of kinship which you do not have except through them. That means being kind to your paternal uncles and your father’s relatives, and to your maternal uncles and aunts, who are your mother’s relatives. This is part of showing kindness to your parents and honouring them, by showing kindness to your father’s relatives, your paternal uncles and aunts and their children, and your maternal uncles and aunts and their children, being generous towards them and upholding ties with them. All of that is part of upholding ties with your parents and honouring them.
End quote from Majmu` Fatawa Ibn Baz, 25/368-369.
As for visiting the grave, that is not stipulated as part of honouring parents. The child can honour his parents by offering supplication for them and by other means even if he is far away from their graves.
Shaykh Ibn `Uthaymin (may Allah have mercy on him) was asked: My father died a long time ago, and his grave is far away from me, and I will not be able to visit it except in two or three years’ time. Can I honour him in any other way when I am so far away?
He replied:
The purpose of visiting the dead is to offer supplication for them, and supplication will reach them from wherever the one who offers the supplication is, because the Prophet (blessings and peace of Allah be upon him) said: “When a person dies, his good deeds come to an end except three: ongoing charity, beneficial knowledge, or a righteous child who will offer supplication for him. So you may offer supplication for your father in any place where you are, near or far, and there is no need to visit his grave. Yes, if you are in the same city for some purpose, and you go and visit your father’s grave, there is nothing wrong with that. As for travelling specifically for the purpose of visiting his grave, that is not allowed.
End quote from Nur `ala ad-Darb, 7/196.
And Allah knows best.