Transit via PEK in January

I hold a Swedish passport and will be travelling from Bangkok (BKK) via Beijing (PEK) to Frankfurt and then further to Zürich on 6th Jan. Our layover in PEK will be 13 hours long, so we're hoping we can leave the airport and go to the city for a few hours. Can you please confirm if I need to apply for a visa for this before travelling or at the PEK airport?

My girlfriend has an American passport, do the same rules apply for her?

Can you point me to where I can read more about this as well? Many thanks for help!