1The first book I wrote, Theophilus, concerned all that Jesus began both to do and to teach, 2until the day in which he was received up, after he had given commandment through the Holy Spirit to the apostles whom he had chosen. 3To these he also showed himself alive after he suffered, by many proofs, appearing to them over a period of forty days and speaking about God’s Kingdom. 4Being assembled together with them, he commanded them, “Don’t depart from Jerusalem, but wait for the promise of the Father, which you heard from me. 5For John indeed baptized in water, but you will be baptized in the Holy Spirit not many days from now.”
6Therefore, when they had come together, they asked him, “Lord, are you now restoring the kingdom to Israel?”
7He said to them, “It isn’t for you to know times or seasons which the Father has set within his own authority. 8But you will receive power when the Holy Spirit has come upon you. You will be witnesses to me in Jerusalem, in all Judea and Samaria, and to the uttermost parts of the earth.”
9When he had said these things, as they were looking, he was taken up, and a cloud received him out of their sight. 10While they were looking steadfastly into the sky as he went, behold, two men stood by them in white clothing, 11who also said, “You men of Galilee, why do you stand looking into the sky? This Jesus, who was received up from you into the sky, will come back in the same way as you saw him going into the sky.”
12Then they returned to Jerusalem from the mountain called Olivet, which is near Jerusalem, a Sabbath day’s journey away. 13When they had come in, they went up into the upper room where they were staying, that is Peter, John, James, Andrew, Philip, Thomas, Bartholomew, Matthew, James the son of Alphaeus, Simon the Zealot, and Judas the son of James. 14All these with one accord continued steadfastly in prayer and supplication, along with the women and Mary the mother of Jesus, and with his brothers.
15In these days, Peter stood up in the middle of the disciples (and the number of names was about one hundred twenty), and said, 16“Brothers, it was necessary that this Scripture should be fulfilled, which the Holy Spirit spoke before by the mouth of David concerning Judas, who was guide to those who took Jesus. 17For he was counted with us, and received his portion in this ministry. 18Now this man obtained a field with the reward for his wickedness; and falling headlong, his body burst open and all his intestines gushed out. 19It became known to everyone who lived in Jerusalem that in their language that field was called ‘Akeldama,’ that is, ‘The field of blood.’ 20For it is written in the book of Psalms,
‘Let his habitation be made desolate.
Let no one dwell in it;’
and,
‘Let another take his office.’
21“Of the men therefore who have accompanied us all the time that the Lord Jesus went in and out among us, 22beginning from the baptism of John to the day that he was received up from us, of these one must become a witness with us of his resurrection.”
23They put forward two: Joseph called Barsabbas, who was also called Justus, and Matthias. 24They prayed and said, “You, Lord, who know the hearts of all men, show which one of these two you have chosen 25to take part in this ministry and apostleship from which Judas fell away, that he might go to his own place.” 26They drew lots for them, and the lot fell on Matthias; and he was counted with the eleven apostles.
There is uncertainty as to whether the Upper Room spoken of in Acts 1:13 is the same one that was used by the twelve disciples and Jesus on the night of the Last Supper before His betrayal of the Upper Room (Matt 26:17-35), or the place the apostles were meeting discussed in Luke 24:33-48. It might also be the one that is spoken of in Acts 1:13. Since Mary, the mother of Jesus, as well as His brothers, it may be that this was their home in Jerusalem, mentioned in Acts 12:12. We simply can't tell from the text. The night of the meeting of the 120, the apostles, some women, Mary, the mother of Jesus, and James and John had gathered. Several matters were discussed, including the betrayal and death of Judas (1:16-20), and the successor to Judas (1:21-26).
At least two possible sites are found in Jerusalem that may have been the Upper Room of the Last Supper or the one in Acts 1, possible house of Mary. There is tradition for both, but the evidence is inconclusive. See photos at Acts 1:13 for these two sites: the Upper Room and traditional house of Mark in the Syrian Orthodox St. Mark's Convent, or the Upper Room above David's alleged tomb on Mt. Zion near the Temple Mount.