Masjid An-Nabawi
“A Journey should not be made (to visit a masjid) except towards three masajids:
The sacred Masjid Al-Haram (Makkah), this masjid of mine Masjid An-Nabawi (Madinah) and Masjid Al Aqsa (in Jerusalem)."
It is a blessing and an honor from Allah that he has enabled you to visit the blessed city of Madinah and in specific the Masjid of the Prophet ﷺ.
Abu Hurairah narrated: That the prophet ﷺ said:
“A prayer in my Masjid (Masjid An-Nabawi) is a thousand times greater than a prayer in any other mosque, except Masjid al-Haram (Makkah)”.
Collected by Imam Muslim in his Sahih
Abu Hurairah narrated: That the prophet ﷺ said:
"Between my house and my pulpit there is a garden from the gardens of Paradise, and my pulpit is on my fountain tank (i.e. Al-Kauthar)."
Collected by Imam Al-Bukhari in his Sahih
This invalidates the prayer of an individual, with the exception of necessary circumstances. This is something the individual should be mindful of, by paying attention to the signs signaling this matter in the Masjid.
It is legislated to visit the grave the Prophet ﷺ to send salaams occasionally and not repetitively. Likewise send salaams to his two companions Abu-Bakr and Omar may Allah have mercy upon them, who are buried right of the Prophet ﷺ.
Making Dua near the area, or toward the grave of the Prophet ﷺ is not legislated.
Abu Hurairah narrated: That the prophet ﷺ said:
“Do not turn your houses into graves, and do not turn my grave into a place of festivity. Send blessings upon me, for your blessings will reach me wherever you are.”
Collected by Imam Abi Dawud in his Sunan