Next month I'm flying DUS-PEK-AKL with a 19.5 hour layover in Beijing. I've read similar threads and got a lot of information from those bit I'm hoping you can help me with some advice for my specific situation.
5.30AM arrival, will be the first time in China for my girlfriend’s and myself so nice opportunity to get a first glimpse. Air China offers a hotel near the airport but I think it’s better to book something in the city so that we’re flexible as in when we need/will try to get some sleep? What’s the perfect 1 day itinerary for our case? And in which area to book a hotel (budget travelers)? Best transport from/to airport?
Next important question, food! Long day so will try to fit at least 2 meals into it of course

.

Obvious choices are duck and dumplings I think? Da Dong & Made in China are reasonably close to interesting areas we will visit I think? Is the price level of those 2 similar? Our day in Beijing will be a Sunday. Need for reservations? And where to go for street food? We like beer so Great Leap Brewing also sounds like a place to add to the list based on other topics.
A month later on the way home it’s SYD-PEK-DUS, 22 hour in Beijing this time with a 4:40AM arrival. That day we want to go visit the Great Wall. We would prefer to go to a not so crowded place where we can do some hiking on the wall.
Mutianyu, or is there a better option? Can someone recommend a driver/guide for transport from the airport? Not sure yet where we will go after the wall for the rest of the day, any ideas?
Lots of questions, hope to get some help, thanks in advance.