All perfect praise be to Allah, The Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad is His slave and Messenger.
The number of Soorahs that were revealed in Makkah are eighty-three Soorahs; it was also said that they are eighty-five, and it was said otherwise.
The number of Soorahs that were revealed in Madeenah are thirty-one Soorahs; it was also said that they are twenty-nine, and it was said otherwise.
Nonetheless, there is no doubt that the number of the Soorahs of the Quran are 114 Soorahs and that the number of Soorahs that were revealed in Makkah were more than those which were revealed in Madeenah. This is because the duration of revelation in Makkah was longer. The entire period of revelation was 23 years: 13 years in Makkah and 10 years in Madeenah.
As regards listing these Soorahs by name and ordering them, then you may refer to the Masaahif (copies of the Quran), which are available – praise be to Allah – everywhere and accessible to everyone.
As-Suyooti mentioned in a number of narrations from the righteous predecessors Al-Itqaan, which we will summarize in the following:
Soorah Al-An‘aam was revealed in Makkah all at once… the following Soorahs were also revealed in Makkah: Al-A‘raaf, Yoonus, Hood, Yoosuf, Ar-Ra‘d, Ibraaheem, Al-Hijr, An-Nahl ... Al-Israa’, Al-Kahf, Maryam, Taahaa, Al-Anbiyaa’, Al-Hajj … Al-Mu’minoon, Al-Furqaan, Ash-Shu‘araa’ … An-Naml, Al-Qasas, Al-‘Ankaboot, Ar-Room, Luqmaan … As-Sajdah, Saba’, Faatir, Yaa-Seen, As-Saaffaat, Saad, Az-Zumar, as well as the seven Soorahs which start with Haa-Meem, Qaaf, Ath-Thaariyaat, At-Toor, An-Najm, Al-Qamar, Ar-Rahmaan, Al-Waaqi’ah, As-Saff, At-Taghaabun … Al-Mulk, Al-Qalam, Al-Haaqqah, Al-Ma’aarij, Nooh, Al-Jinn, Al-Muzammil ... and from Al-Mudath-thir until the end of the Quran with the exception of Az-Zalzalah, An-Nasr, Al-Ikhlaas, Al-Falaq, and An-Naas, which were revealed in Madeenah.
The following Soorahs were also revealed in Madeenah: Al-Anfaal, At-Tawbah, An-Noor, Al-Ahzaab, Muhammad, Al-Fat-h, Al-Hujuraat, Al-Hadeed, and all the Soorahs that came after it until Soorah At-Tahreem.
There were other narrations that were reported from Ibn ‘Abbaas, may Allah be pleased with him, and others in this regard, but this is not the place to mention them.
Allah knows best.