Do I need transit visa in China if I want to leave the airport for about 9 hours?

Hi, I´m Slovak citizen, living in UK now. I´m travelling from UK to South Korea and I need to transfer in Beijing. I´ve got about 10 spare hours there, on my way back to UK. I´d like to leave the airport and see a bit of Beijing,
1. Do I need transit Visa? And if so, I´m running a bit of time, because my flight is already in two days to South Korea.
2. Could I ask for it in Seoul?
3. And is it cheaper then tourist visa? or is it the same?
thank you very much