The best spot on earth in general terms is Makkah, then Madinah, but the best place to live on earth for each person is the spot where he is most able to obey Allah and His Messenger
Question

What is the best place that Allah has made on this earth? I told someone that it was Mecca, but the person argued and said that it is Medina. The person reasoned that the Prophet (blessings and peace of Allah be upon him) loved Medina more than Mecca and asked Allah to bless Medina as he blessed Mecca.
Praise be to Allah.Firstly: 
The fuqaha’ are unanimously agreed that Makkah and Madinah are the best spots on earth, then they differed as to which of them is best. The majority of fuqaha’, including the Hanafis, Shaafa‘is and Hanbalis – and it is also an opinion held by some Maalikis – are of the view that Makkah al-Mukarramah is superior to al-Madinah al-Munawwarah, for a number of reasons which were listed by the scholars: 
1.The fact that it is obligatory to go there for Hajj and ‘umrah, which are two obligatory duties for which there is no equivalent that happens in Madinah.
2.Although Madinah was distinguished by the fact that the Messenger of Allah (blessings and peace of Allah be upon him) settled there after Prophethood, Makkah is superior to it, because the Prophet (blessings and peace of Allah be upon him) stayed there for thirteen years after his Prophethood began, and he stayed in Madinah for (only) ten years.
3.Although Madinah is distinguished by the large number of visitors from among the righteous slaves of Allah, Makkah is superior to it because of the large numbers from among the Prophets, Messengers and the righteous who visited it.
4.Kissing and touching are acts that are uniquely connected to the two Yemeni corners [of the Ka‘bah, i.e., the corner where the Black Stone is and the Yemeni Corner], and there is nothing comparable in Madinah.
5.Allah, may He be glorified and exalted, has instructed us to face towards Makkah in prayer wherever we may be, in any city or in the wilderness, but no such requirement is made of us with regard to Madinah.
6.Allah made Makkah a sanctuary on the day He created the heavens and the earth, and it was not permissible for any of the Messengers and Prophets [to fight therein] except our Prophet (blessings and peace of Allah be upon him), out of all the other Prophets, and it was only made permissible for him for a short time of one day.
7.Allah, may He be glorified and exalted, praised the House (the Ka‘bah) in His Book in a manner in which He did not praise Madinah, as He said (interpretation of the meaning): “Verily, the first House (of worship) appointed for mankind was that at Bakkah (Makkah), full of blessing, and a guidance for Al-Alameen (mankind and jinns)” [Aal ‘Imraan 3:96].
8.One prayer in al-Masjid al-Haraam in Makkah is equivalent to one hundred thousand prayers offered elsewhere, and nothing similar is true in the case of the Mosque of the Prophet (blessings and peace of Allah be upon him) in Madinah or any other mosque.
And there are other virtues by which Makkah is superior to Madinah. 
The well-known view among the Maalikis is that Madinah is superior to Makkah. Al-Hattaab said: This – i.e., the view that Madinah is superior to Makkah – is the view of the majority of the people of Madinah. 
They are also unanimously agreed that the Ka‘bah is superior to Madinah, apart from the noble grave, blessings and peace be upon its occupant. 
See: al-Mawsoo‘ah al-Fiqhiyyah (32/154-156) 
Undoubtedly the Ka‘bah is superior to the grave of the Prophet (blessings and peace of Allah be upon him) itself. Shaykh al-Islam Ibn Taymiyah (may Allah have mercy on him) was asked about two men who disputed: one of them said that the ground where Muhammad the Prophet (blessings and peace of Allah be upon him) is buried was superior to the heavens and the earth, and the other said that the Ka‘bah was superior; which one was correct? 
He replied: 
As for Muhammad himself (blessings and peace of Allah be upon him), Allah has not created anything or anyone that is dearer to Him than him. 
As for the grave itself and the ground where he is buried, it is not superior to the Ka‘bah, the Sacred House; rather the Ka‘bah is superior to it. It is not known that any of the scholars regarded the ground of the grave as superior to the Ka‘bah, apart from al-Qaadi ‘Iyaad; no one suggested that before him and no one agreed with him on that. And Allah knows best.
End quote from Majmoo‘ al-Fataawa (27/38) 
The more correct of the two opinions on this matter is that of the majority of scholars, which is that Makkah is superior to Madinah in general terms. As-Suyooti (may Allah have mercy on him) wrote an essay dealing with this topic, which has been printed under the title: al-Hujaj al-Mubeenah fi Tafdeel Makkah ‘ala al-Madinah (Clear Proof of the Superiority of Makkah over Madinah). 
Shaykh Ibn Baaz (may Allah have mercy on him) was asked: 
Which is better, to stay in Makkah or in Madinah for the purpose of worship? 
He replied: 
Makkah is best, followed by Madinah. Staying in Makkah is best, followed by Madinah, as it says in the hadeeths; one prayer in Makkah is equivalent to one hundred thousand prayers (offered elsewhere). The Prophet (blessings and peace of Allah be upon him) said concerning Madinah: “One prayer in this mosque of mine is better than a thousand prayers offered elsewhere, except in al-Masjid al-Haraam. One prayer in al-Masjid al-Haraam is equivalent to one hundred thousand prayers (offered elsewhere).” This is a great difference. Good deeds in Makkah are many times greater (in reward) than in Madinah.
End quote from the Shaykh’s website.
With regard to anyone saying that the Prophet (blessings and peace of Allah be upon him) loved Madinah more than Makkah, if what he means is loving to settle there, then yes; staying there better served the important purpose of spreading the religion and establishing the foundations of the Islamic state, and because it is the place to which he migrated, and because Makkah at that time was the headquarters of disbelief and its people. 
But that on its own does not indicate that Madinah in and of itself is superior to Makkah in all aspects. 
Al-Bukhaari (3926) and Muslim (1376) narrated from ‘Aa’ishah (may Allah be pleased with her) that the Prophet (blessings and peace of Allah be upon him) said: “O Allah, make Madinah dear to us as you made Makkah dear, and more so. Make it healthy and bless us in its saa’s and muds [units of measurement]. 
Al-Baaji (may Allah have mercy on him) said:
This is a supplication from the Prophet (blessings and peace of Allah be upon him) asking Allah to take away what they felt in their hearts of homesickness for having left Makkah and settled in Madinah, and asking Allah to make Madinah as beloved to them as Makkah was, so that they would dislike to move from it as they had disliked to move from Makkah.
End quote from al-Muntaqa (7/194) 
This supplication of the Prophet (blessings and peace of Allah be upon him) was only because of what his companions were suffering from of the fever of Madinah, so he prayed that they would love to stay there and hate to move from it.
For more information, please see the answers to questions no. 36863 and 106609 
And Allah knows best.