Is there a New Testament parallel to cities of refuge? Many things in the Old Testament have a New Testament parallel. For example, the OT has animal sacrifices. In the NT, Jesus is described as the Lamb of God, sacrificed for sins. 

My question: I find cities of refuge mentioned in Numbers 35. Have published commentators found any NT spiritual parallel to this idea?
Yes.


  Hebrews 6:16 (KJV)
  That by two immutable things, in which it was impossible for God to lie, we might have a strong consolation, who have fled for refuge to lay hold upon the hope set before us:


Matthew Henry's commentary on this verse points to Jesus as our present refuge:


  They are such as have fled for refuge to the hope set before them.
  Under the law there were cities of refuge provided for those who were
  pursued by the avenger of blood. Here is a much better refuge prepared
  by the gospel, a refuge for all sinners who shall have the heart to
  flee to it; yea, though they have been the chief of sinners.