My idea is very simple, and it addresses the 2 biggest concerns I see with reusable coffee cups as they are right now:

1. They are hard to keep clean (it's hard to find a place to clean them)
2. They can be tricky to pack around

My suggested solutions:

1. Set up cup cleaning stations at every coffee shop. The main issue really isn't the cup - it's the lack of cleaning facilities for the cup. People don't want to go into the washroom to clean their cups. Coffee shops need a handy cup cleaner available so that people can clean their cups before use to have a fresh cup for their next refill, and after use so they can safely pack it home without coffee spilling onto their clothes or belongings.I suggest a small automated enclosed unit into which you place your cup and lid. It then washes and dries both the inside and the outside of your cup, as well as the lid. I foresee a small plexiglass cube style setup that accommodates the usual sizes of cups with an additional spot for the lid. Jets inside and outside of the cup clean and sanitize the cup and lid. Then an air drying system similar to what is used to dry hands in the washroom should dry the cup. The whole process must take no more than a few seconds.

2. The cup should be light and easy to pack. I suggest something similar to the collapsible kitchenware that is already available. It must be rigid and stable when full sized, yet collapse to a fraction of the size so it fits into a purse or pocket easily. The design should include a lid as always. The design must also be easily able to withstand the temperatures of the cleaning, sanitizing, and drying process of the cleaning station.
In practice:People walk into the coffeeshop with their reusable cup. Before getting to the front of the lineup they set their cup into the cleaning station which prepares the cup for use. They get their coffee and then either leave with it, or they stay and finish their coffee. Those who finish their coffee will then have the chance to use the cleaning station again before leaving, so that their is no chance of residual beverage getting onto their clothes and belongings.