If your time is limited and all you want to do is walk the Great Wall of China, a terrific way to get to the best (read least crowded) part of the Wall from the airport is to travel with the locals, by public bus (not tour bus/private car/ organised tour).
From the airport, take the express to Dongzhimen station. Takes about half an hour; costs 25RMB. Take 916 express (make sure it’s the EXPRESS) – to Huairoubeidajie station, transfer to H23 or quick cab ride to Mutianyu and head to Tower 14. Making the bus easy
Or get the bus all the way up & (still) head to Tower 14, then just keep climbing.
You can go all the way to the top. It takes a bit of effort, but is soooooo worthwhile. I even had large portions of the wall to myself, sometimes for several minutes at once (when I wasn’t sharing it with a bride in a beautiful red dress and her groom, photographer and assistants)..
There’s not much food, and it’s a bit arduous(can something be a bit arduous?), so take some food with you or there is the chance to bargain for water, fruit and snacks on the way up, if you forget. And there are drink sellers right near the top – hardy souls, I think they deserve patronage.
Such an achievement to climb so high, you feel like you are on top of the world.
and if you get to Shanghai
If you have time to visit Shanghai, aside from my favourite restaurant – Mr and Mrs Bund where this desert takes three days to prepare –
there are two out-of-the-way places you should visit – the well-hidden propaganda poster museum
and the equally inconspicuous Former Provisional Government Site of the Republic of Korea (reminded me a little of the Churchill War Cabinet rooms in London)