When does a passenger plane leave the cruising phase?
The distinction when you cross from one phase to another is somewhat arbitrary.  However, you can slice this multiple ways depending on your goal:  The approach phase could be considered to start at the first point of a published STAR, (Standard Arrival) the initial approach fix of a published instrument approach procedure, when the pilot descends below the class A airspace, i.e. &lt;18,000' MSL, or the first ATC assigned vector off the filed route.  (Or some radius as you suggested...)  

If you really want to dig into this my recommendation is to go to a local pilot shop and purchase a set of Approach Plates/STARS and a high altitude IFR chart for the area you are interested in.  You will likely need help interpreting them if you are unfamiliar with these publications.  

If you then have a specific question on your airport of interest there are plenty of experienced people here who are willing to help, but a full education on high altitude IFR enroute and terminal arrival procedures is beyond the scope of this forum.  

In lieu of that, if you don't want to take that kind of time to learn something foreign but have a specific airport you are interested in analyzing, please let me know.  I have a full set of United States procedures loaded in my iPad EFB and would be happy to post a screenshot with an interpretive description of where I might consider the approach phase to begin for a specific airfield/runway combination.  

There are many many different arrival procedures nation wide, into airports of varying levels of traffic congestion.  Without a better understanding of your actual goal the question as stated is almost to broad to answer, especially for someone who is admittedly "not too deep into aviation".  Good luck with your project.