Staying for 18 hrs

Hi, I'm going to transit to Beijing for my connected flight from South Korea to Los Angeles, CA. I'm a Filipino citizen and I wanted to look around Beijing for a while. Do I have to apply for a transit visa in the Chinese Embassy here in Seoul? Or I can apply for a free transit in the Airport? Or should I stay in the airport for 18 hrs (which is very boring)? Thank you! Have a nice day!