Wa Alaykum Assalam and thank you for your question.
Some scholars completely forbid visiting the graves of saints, while others allow it provided that the Muslim avoids certain rituals that are acts of shirq (associating other lords with Allah).
What is the Muslim’s intention from visiting graves of saints and leaving food at such sites? This is the question that needs to be addressed because we are judged by our intentions.
Is it because we feel that our dua is better accepted? This is a big misconception.
Is it to make dua to the deceased or to ask dua from him? We need to ponder upon the meaning of the duas that we say. If they address the Saint directly then how could we possibly ask from a dead person to help us when we are taught by our Prophet (peace be upon him) that his deeds have halted.
Fadalah bin ‘Ubaid (May Allah be pleased with him) reported that the Messenger of Allah (peace be upon him) said:
“The actions of every dead person come to a halt with his death except the one who is on the frontier in Allah’s way (i.e. observing Ribat). This latter’s deeds will be made to go on increasing for him till the Day of Resurrection, and he will be secure from the trials in the grave.” (Abu Dawud and At-Tirmidhi)
The only exception is the one who was in Jihad protecting the frontier of the Muslim lands. Does the saint fall under this category?
Finally, the Prophet (peace be upon him) advised us not to just go on a journey for the purpose of visiting any house of worship. Abu Hurairah (Allah be pleased with him) reported it directly from Allah’s Apostle (peace be upon him) that he said:
“Do not undertake a journey to visit any Mosque, but three: this Mosque of mine, the Mosque of al-Haram and the Mosque of Aqsa (Bait al-Maqdis). (Sahih Muslim)
In addition, most of these shrines are actually masjids where the saints’ graves are located within their boundaries such that people prostrate to the grave during prayers or otherwise; while we are warned not to do so, even for the Prophet (peace be upon him); It was narrated from Aishah that the Prophet (peace be upon him) said:
“May Allah curse people who take the graves of their prophets as Masjids.” (An-Nasai, Sahih)
Please note that the Prophet’s grave in Madinah is placed in the far corner of the Masjid that no one prostrates in front of it.
If we ponder upon the above mentioned, we realize that there is no good purpose from visiting the graves of saints (mazaar). We visit graves to remind us of death and ask forgiveness for the deceased.