The caliphate is in Madinah and the kingship in Syria

It is narrated from Sayyiduna Safinah (may Allah be pleased with him); he said: When the Messenger of Allah (peace and blessings be upon him) had prayed the Fajr prayer, he would ask: "Has any of you seen a dream last night?" One day he (peace and blessings be upon him) led the Fajr prayer, then turned to his Companions and asked: "Which of you has seen a dream?" A man said: "O Messenger of Allah, I saw as if a balance was lowered from the sky. You were placed in one pan and Abu Bakr in the other pan, and your side outweighed Abu Bakr. Then you were lifted away and Abu Bakr remained in his place. Then Umar bin al-Khattab was brought and placed in the other pan, and Abu Bakr's side outweighed Umar. Then Abu Bakr was lifted away and Umar remained in his place. Then Uthman bin Affan was brought and placed in the other pan, and Umar's side outweighed Uthman. Then both of them were lifted away, and the balance was lifted away too." The narrator said: (On hearing this) the colour of the blessed face of the Messenger of Allah (peace and blessings be upon him) changed. Then he (peace and blessings be upon him) said: "The caliphate of prophethood will last thirty years; after that there will be kingship." Sa'id bin Jumhan said: Safinah (may Allah be pleased with him) said to me: Count (these years): two years of Abu Bakr, ten years of Umar, twelve years of Uthman and six years of Ali (may Allah be pleased with them all).
This dream has also been narrated with an authentic chain as a marfu' report from the Prophet (peace and blessings be upon him).

It is narrated from Sayyiduna Jabir bin Abdullah (may Allah be pleased with them both) that the Messenger of Allah (peace and blessings be upon him) said: "Last night a righteous man was shown in a dream that Abu Bakr was joined to the Messenger of Allah (peace and blessings be upon him), Umar was joined to Abu Bakr, and Uthman was joined to Umar." Sayyiduna Jabir (may Allah be pleased with him) said: When we got up from the presence of the Prophet (peace and blessings be upon him), we said: The "righteous man" is the Prophet (peace and blessings be upon him) himself, and the mention of their being joined to one another indicates that they will be the governors of this matter (the caliphate) with which Allah sent His Prophet (peace and blessings be upon him).
The last part of this hadith has an authentic chain from Sayyiduna Abu Hurayrah (may Allah be pleased with him), but the two Shaykhs (Bukhari and Muslim) did not record it.

It is narrated from Sayyiduna Abu Hurayrah (may Allah be pleased with him) that the Prophet (peace and blessings be upon him) said: "The caliphate will be in Madinah, and kingship will be in Sham (Syria)."

It is narrated from Sayyiduna Ali bin Abi Talib (may Allah be pleased with him) that the Messenger of Allah (peace and blessings be upon him) said: "May Allah Almighty have mercy on Abu Bakr. He gave me his daughter in marriage and carried me to the abode of emigration (Madinah)."
This hadith is sahih (authentic) on the condition of Imam Muslim, but the two Shaykhs (Bukhari and Muslim) did not record it.

It is narrated from Sayyiduna Abdullah bin Umar (may Allah be pleased with them both) that when the Messenger of Allah (peace and blessings be upon him) entered (Makkah) in the year of the Conquest, he (peace and blessings be upon him) saw women striking the faces of the horses with their veils. He (peace and blessings be upon him) looked at Sayyiduna Abu Bakr (may Allah be pleased with him), smiled and asked: "O Abu Bakr, what did Hassan bin Thabit say (about this)?" So Sayyiduna Abu Bakr (may Allah be pleased with him) recited these verses to him: "May I lose my daughter if you do not see them (the horses) raising dust from both sides of Kada', pulling at the spears as they race, while the women strike them with their veils." Then the Messenger of Allah (peace and blessings be upon him) said: "Enter from where Hassan mentioned."
This hadith is sahih (authentic) in its chain of narration, but the two Shaykhs (Bukhari and Muslim) did not record it.

It is narrated from Sayyiduna Abdullah bin Mas'ud (may Allah be pleased with him); he said: We were sitting with the Prophet (peace and blessings be upon him) when he (peace and blessings be upon him) said: "A man from the people of Paradise is about to appear before you." Then Sayyiduna Abu Bakr (may Allah be pleased with him) appeared, gave the greeting of peace and sat down.
This hadith is sahih (authentic) on the condition of Imam Muslim, but the two Shaykhs (Bukhari and Muslim) did not record it.