23 hour layover

Your itinerary is definitely eligible for 24 hour visa free transit. I understand that you know this detail and you are looking to be allowed to exit the airport and to enjoy a quite night with good sleep. You can rely on two options and you will decide which one will you choose:

- You can apply for 24 hour free entry permit upon your landing in Beijing. This option is totally free and you are supposed to bring a confirmation of your accommodation booking at the moment of your application. So, have this confirmation in hard copy. Anyway, you should be aware that the issuing of entry permit is not a passenger's right, but it depends entirely upon immigration authorities discretion. The practice has shown that the largest majority of passengers, having with them a booking confirmation in hard copy, are granted an entry permit. Your chances for that are really very, very good.

- You can apply in advance for Chinese transit (G) visa in advance at relevant Chinese visa issuing institution. Of course, as US citizens, you can also apply for 10 year multiple entry tourist (L) visa that can be very useful for your travels in the future. With any of the mentioned visas, you will be definitely allowed to exit the airport.

Now, when you know your options and circumstances, it's up to you to decide.