If I go to a coffee shop to do a bit of work on the WiFi, is it legit to buy the requisite coffee or two on my company card and treat it as a business expense?
That's honestly more of a semantics question. The IRS doesn't appreciate it but, they're not going to kill you for it. Whatever you spend on coffee is only going to be 50% deductible under meals and entertainment, so don't worry about it.