There is some confusion as to the identification and location of paradise. This is because the word itself is used in more than one way. 

For example, in Revelation 2:7 we read of the tree of life in the midst of the paradise of God. This usage obviously refers to heaven.

However, in the passage given in your inquiry (Luke 23:43) Jesus uses the term in a different way. The paradise of Luke 23:43 is a part of the hadean realm. In Luke 16:19-31, Jesus taught that our spirits leave our bodies at the time of death. Also, James 2:26 says, "For as the body without the spirit is dead, even so faith without works is dead also."

Luke 16:19-31 also teaches us where our souls go at death. According to this text, all the dead go to the hadean realm (Hades) and await the Judgment. 

This is what Jesus taught in the story of the Rich Man and Lazarus. 

According to this text, Hades is divided into two dwelling places, one for the righteous and the other for the unrighteous. The place of the righteous is a place of comfort (v 25) described as Abraham's bosom (v 22). From the cross, Jesus referred to this place as Paradise (Luke 23:43). The waiting place of the unrighteous is a place of torment (vv 23-25, 28). Peter calls this place Tartarus in 2 Peter 2:4 (cf Jude 6). Most scholars agree that torment and Tartarus are the same place. Paradise and Torment are separated by a great impassible gulf (Luke 16:26).

There is a third use of Paradise in 2 Corinthians 12:4. I will be honest I am unsure as to which usage is intended here, but I lean strongly toward the heavenly usage and not the hadean.

As with any word used in different ways, we must allow the context to determine the intended meaning of the text.