All the countries around Syria have received refugees. UN figures as of Dec 14. Why is the overflow not going to Saudia? Simple, geography. Most refugees can only flee north, as they cannot pass south of Damascus due to Assad's forces. They cannot go east due to ISIS. East is how they would get to Saudia. North from Homs & Aleppo is the only safe route left for the majority fleeing the conflict.
Lebanon hosts 1.1 million refugees registered with UNHCR, which amounts to around 26 per cent of the country’s population
Jordan hosts 618,615 registered refugees, which amounts to 9.8 per cent of the population
Turkey hosts 1.6 million refugees, which amounts to 2.4 per cent of the population
Iraq hosts 225,373 registered refugees, which amounts to 0.67 per cent of the population
Egypt 142,543 registered refugees, which amounts to 0.17 per cent of the population