The Assumption of Mary states that after she died on Earth she went to Heaven.
Is there any Biblical support whether she, or any other man after Jesus' revival went to heaven?
I would like to explain what I understand about Heaven.
I believe that Paradise was a place where the Old Testament saints were waiting for Jesus to defeat Satan and bring them to Heaven. The first person to enter Paradise would be Abel and the last would possibly be the thief crucified at the right hand side of Jesus on the cross. Abraham was a notable figure there in paradise as we see in
Heaven is not the permanent place where the believers will stay. God has a greater plan for all believers. God will create a New Earth for his holy people. Apostle John saw this future planet Earth in his vision.
Revelation 21:1-4 (NIV)
Thus, there are 3 places appointed for the saints.
Let's talk about Hell.
Paradise and Hell (Sheol) were very close to each other as we see in Luke 16:19-31. Any one who disobeys God in the OT times were in Hell. Now everyone who rejects Jesus Christ as their savior are in Hell. We don't know the first one to enter Hell but one of the first would be Cain. After the judgment day, all the people in Hell will be thrown into the Lake of Fire.
Revelation 20:11-15 (NIV)
The main verse that people quote with regards to being in heaven immediately is the words of Jesus on the cross to the thief:
Indicating that rather than just waiting until the 2nd coming, there is a paradise which people inhabit immediately upon death, similar to that spoken of in John 14:2, where the phrase indicates more of a temporary dwelling than a permanent one.
However, this would also seem to be separate from the Heaven described elsewhere in places like Revelation, as the descriptions involving God's people inhabiting Heaven all come after the 2nd coming
There's a difference between being in heaven completely (with body) and with soul only. We have biblical evidence for the first in case of Enoch (Genesis 5:24) and Elijah (2Kings 2:1-18), there is an apocryphal account of this happening to Moses (Assumption of Moses) and the tradition dogmatized in Catholic Church and believed by many in Orthodox Churches claims that something similar happened to Mary. It happened sometime near the end of the Acts of Apostles plotline, and since Acts doesn't tell us even about acts of most apostles (but mostly about Peter and Paul), it's no wonder that Mary's assumption wasn't recorded in books of canonic Bible, but only in an oral tradition.
About being in Heaven by soul only, Matt Taylor already addressed it qite well.