My idea is extremely simple.  Make completely biodegradable/recyclable cups.  Then put Recycling bins in the Starbucks stores.  I've never seen a recycle bin in a Starbucks store and I always thought this was odd since they sell glass, plastic and aluminum bottled drinks and use plastic for their cold drinks. 

If you want people to recycle they shouldn't have to carry their garbage with them to their home or office or school or wherever they are going.  This is  very very basic and I'm surprised Starbucks hasn't figured it out yet!

To go along with this they also don't ask if it's for here or to go and give out reusable mugs for customers staying in.  This practice encourages waste.  It would be simple to ask the question "For here or to go?" and give cups out accordingly. 

This doesn't really require changing much at all and should be a very simple thing to incorporate into the Starbucks Culture.