Did you know the Starbucks paper coffee cups are not recyclable? Although they feel like paper, they are actually lined on the inside with a thin coating of plastic to help stop the cup from soaking through, and recycling places only accept them in bulk. And since most people leave with their cups, Starbucks does not recycle them, and neither does your regular trash pick up.
The only way to make the whole cafe mocha process more eco-friendly is to go ahead and purchase one of their permanent plastic coffee "travelers" for sale, which are dishwasher safe and can be used again and again.
I'm never one to shill for Corporate America, but I've been taking those stupid Starbucks "paper" coffee cups out of the store for years and carefully washing them and putting them in the recycling bin at home once they were empty. All for naught, it turns out. In order to be part of the solution, not the problem, we should really have invested in a few of those plastic travelers for purchase and just re-used them.
Oh course if your tastes run more towards the cold drinks, you are safe. The large plastic "glasses" they serve those in ARE recyclable. So take the cold mocha frappucino over the warm latte, I suppose, until you break down and buy yourself a re-usable hot coffee container.
Of course, I guess we could always show up with a Mason Jar and see if they'd fill that. Might be worth it, if just to see the reaction from the barista behind the counter.