Is a transit visa needed if I go out of the airport?

we are travelling through Beijing with an overnight transit time of 15 hours at Beijing airport (PEK) terminal 3.
Can we leave the airport to stay at a nearby hotel without a visa?
If there is a transit visa how do I get one. On the china embassy website there was no form for a transit visa.

If not is there a room within the terminal that we can book?