The UNHCR has provided a portal for tracking when refugees have left Syria and where they have gone. The display of data in the graph below is in no way endorsed by the UNHCR, but was aggregated from their portal
As seen in a previous post, neighboring countries and specifically Lebanon has played a significant role in the process of relocating refugees. The flow of people to these countries over time is remarkable considering that the demographics of most refugees entering neighboring countries, over 50% of the refugees are under the age of 18 (validity of this number also available at the UNHCR portal). The chart below is interactive, but set to a setting that shows the growth over time of refugees from Syria moving to other countries. You may notice the specific months where this spikes as well. The data from the portal began in 2011 for the countries being tracked, and at that point some countries were already facilitating camps or other accommodations for Syrian refugees.