I have been to Beijing several times on Megacorps' dime. Generally speaking I had no problems, no more so that in any large city. Traffic can get crazy, but having grown up in a city I was used to it. I had no problems with people, even though I am not a blue eyed blond haired American.
If you can pick up some of the language and even try, that goes a long way. There are also many there who are happy to speak English with you as they want to learn to speak it better. My DW is fluent in Chinese, and when she went with her university group she made lots of friends (and many in the group would not go anywhere without her).
You do have to accept that you are being watched, and your hotel room is probably bugged and will be searched. Popular internet sites like anything Google and Facebook are blocked (there are ways to get around it using VPN, but I figured why tempt fate). Being watched, though, has its "good" side - they really do not want to see anything happen to foreign visitors so I felt very safe there. However, on one project I worked on a couple of folks could not get visas to return for the second phase of the project - apparently they took to the "wild night life" - whatever there is of it - and it was noticed.
The major cultural aspect I could not get used to was "clustering" instead of lines in many places.
However, I am glad I am a Yankees fan - wearing that logo got me lots of smiles and thumbs up from the locals, even the police.
DW and I have been there separately but never together... a joint trip is something we would consider. It is easier when you can go to places not assuming they are like where you grew up, and are open to learning and sharing with them at the personal level, in an inoffensive manner.