The best way to reduce the waste generated by to-go cups is to not use to-go cups. Many businesses have discounts for bringing your own cup but they aren't strongly advertised and a lot of consumers aren't motivated enough to do so.
We think that if companies offer a free drink if you bring your own cup on a certain day, it could be used as a good promotion tactic and can train people to start bringing their own cups.
A lot of waste can be avoided if people change their consumption habits. However habits are hard to change and trying to get everyone to stop using to-go cups is incredibly hard. Hence, we believe in using baby steps. By having these BYOC (bring your own cup) promotions, consumers can be slowly influenced into reflecting on the waste they generate and changing their habits.