less than 24 hrs layover in Beijing airport

Hi,

I will be arriving to Bejing from the US at around 6pm and then flying to Geneva on the next day at 1:30pm. I am not a citizen of a country with the 72 hrs transit visa waiver programme. I am allowed to leave the airport? Would I be allowed to stay in the transit zone for this layover? Is there a hotel inside the transit costs and how much does it cost?
Thank you,

Alex